on the langlands functoriality for automorphic forms this is the extended notes of my lcctures on the langlands functoriality of automorphic forms which are in particular on the topics closely related to my recent work

periods of residual automorphic forms abstract we develop a technique for computing period integrals of noncuspidal automorphic forms applications include a formula for the integral of a square integrable automorphic form on gl n a e over gl n f gl n a f 1 for a quadratic extension e of a number field f and a characterization of residual automorphic representations on which the period integral is nonvanishing

on a class of nonlinear dispersive dissipative interactions abstract we study a prototype dissipative dispersive equation ut a um x un xxx uk xx a consts which represents a wide variety of interactions at the critical value k m n 2 which separates dispersive and dissipation dominated phenomena these effects are in a detailed balance and the patterns formed do not depend on the amplitude in particular when m n 2 k 1 the equation can be transformed into a form free of convection and dissipation making it accessible to analysis both bounded and unbounded oscillations as well as solitary waves are found a variety of exact solutions are presented with a notable example being a solitary doublet for n 1 and a 2 3 2 the problem may be mapped into a linear equation leading to rational periodic or aperiodic solutions among others

torsion homology growth and cycle complexity of arithmetic manifolds let m be an arithmetic hyperbolic 3 manifold such as a bianchi manifold we conjecture that there is a basis for the second homology of m where each basis element is represented by a surface of low genus and give evidence for this we explain the relationship between this conjecture and the study of torsion homology growth

galois representations arising from some compact shimura varieties our aim is to establish some new cases of the global langlands correspondence for glm along the way we obtain a new result on the description of the cohomology of some compact shimura varieties let f be a cm eld with complex conjugation c and

selberg s orthogonality conjecture for automorphic l functions let and be automorphic irreducible unitary cuspidal representations of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i respectively assume that either or is self contragredient under the ramanujan conjecture on and we deduce a prime number theorem for l s inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i which can be used to asymptotically describe whether or det i 0 for some nonzero 0 inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i or det it for any t inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i as a consequence we prove the selberg orthogonality conjecture in a more precise form for automorphic l functions l s and l s under the ramanujan conjecture when m m 2 and and are representations corresponding to holomorphic cusp forms our results are unconditional

dissimilarity judgments in relation to temporal and spatial factors for the sound field in an existing hall in relation to the temporal and spatial factors of sound fields dissimilarity judgments for different source locations on a stage were performed this study is based on the model of the auditory brain system which consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemispheres there are three temporal factors 1 1 and e extracted from the autocorrelation function and four spatial factors ll iacc iacc and w iacc from the interaural crosscorrelation function of binaural signals in addition to these temporal and spatial factors the orthogonal factors of the subjective preference for sound field t 1 and t sub were taken into account the psychological distance between sound fields of different source locations on the stage were calculated by using these temporal spatial and orthogonal factors of sound fields using these distances and their linear combination dissimilarity can be calculated results of multivariable analysis show that the calculated scale values of dissimilarity agree well with the measured scale values

cubic unipotent arthur parameters and multiplicities of square integrable automorphic forms l g f g a ld g f g a lcont g f g a into the direct sum of its discrete spectrum and its continuous spectrum the theory of eisenstein series reduces the description of lcont g f g a to that of the discrete spectrum of certain reductive subgroups of g and thus the basic question is the understanding of the discrete spectrum ld g f g a the discrete spectrum has a further orthogonal decomposition

nonlinear response in evaluating the subjective diffuseness of sound fields tests were conducted to determine which horizontal reflection angles are most effective in stimulating subjective diffuseness for a listener in a room paired comparison tests were carried out where subjects were asked to judge in which of two sound fields they perceived more diffuseness results show that the most effective horizontal angle depends on the frequency of the one third octave band noise as is indicated by the interaural cross correlation the remarkable finding in this investigation is that the scale value of subjective diffuseness may be formulated in terms of the 3 2 power of the magnitude of interaural cross correlation iacc and that the scale value does not vary with the frequency of the bandpass noise source

global jacquet langlands correspondence multiplicity one and classification of automorphic representations in this paper we generalize the local jacquet langlands correspondence to all unitary irreducible representations we prove the global jacquet langlands correspondence in characteristic zero as consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of gl n as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by m glin waldspurger and jacquet shalika for gl n

the local converse theorem for so 2n 1 and applications in this paper we characterize irreducible generic representations of so 2n 1 k where k is a p adic field by means of twisted local gamma factors the local converse theorem as applications we prove that two irreducible generic cuspidal automorphic representations of so 2n 1 a where a is the ring of adeles of a number field are equivalent if their local components are equivalent at almost all local places the rigidity theorem and prove the local langlands reciprocity conjecture for generic supercuspidal representations of so 2n 1 k

on the voronoi formula for gl n we prove a general vorono u i formula for cuspidal automorphic representations of rm gl n over number fields this generalizes recent work by miller schmid and goldfeld li on maass forms our method follows closely the adelic framework of integral representations of l functions the proof is flexible enough to allow ramification and we propose possible variants for example the assumption that the additive twist is trivial at places where the representation is ramified is sufficient to obtain an explicit final statement with hyper kloosterman sums

weierstrass s criterion and compact solitary waves weierstrass s theory is a standard qualitative tool for single degree of freedom equations used in classical mechanics and in many textbooks in this brief report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist in the framework of continuum mechanics these differential equations correspond to bulk shear waves for a special class of constitutive laws

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

on the generic part of the cohomology of compact unitary shimura varieties the goal of this paper is to show that the cohomology of compact unitary shimura varieties is concentrated in the middle degree and torsion free after localizing at a maximal ideal of the hecke algebra satisfying a suitable genericity assumption along the way we establish various foundational results on the geometry of the hodge tate period map in particular we compare the fibres of the hodge tate period map with igusa varieties

compact solitary waves in linearly elastic chains with non smooth on site potential it was recently observed by saccomandi and sgura that one dimensional chains with nonlinear elastic interaction and regular on site potential can support compact solitary waves i e travelling solitary waves with strictly compact support in this paper we show that the same applies to chains with linear elastic interaction and an on site potential which is continuous but non smooth at minima some different features arise in particular the speed of compact solitary waves is not uniquely fixed by the equation we also discuss several generalizations of our findings

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

regular trace formula and base change lifting introduction the selberg trace formula has become a major tool in the study of automorphic forms on reductive groups although its underlying principle of computing traces of representations by means of orbital integrals is very simple the standard expressions for this important formula are rather complicated this makes applications hard to accomplish the complexity of the expression for the formula may be due to the choice of truncation made in its proof it would be advantageous to have a simple expression for the formula at least for a set of test functions which is sufficiently large for applications the possibility of its existence was suggested to us by some of kazhdan s striking work on the trace formula see e g the density theorem of kl appendix or the study of lifting in k2 here we derive an asymptotic expression of this nature in the simplest case of gl 2 for test functions with a component which is sufficiently regular with respect to all other components we obtain a simple practical form of the trace formula more precisely if fu is a nonarchimedean local field and m 2 1 is an integer we say that a locally constant function f on gu gl 2 fu which is supported on a compact mod center is m regular if it vanishes outside the open closed subset sm zg g g in gu a z in f x with i a 1 r denotes a uniformizer in f x of gu and its normalized orbital integral f g fu a g 4 g fu is the characteristic function of sm in g14 if f is a global field u is a nonarchimedean place of f and fu f is a product over all places v u of f of smooth compactly supported mod center functionsfv on gv such thatfv is the unit elementf v of the hecke algebra for almost all v then we show that there exists mr0 mo fu such that for any m 2r mo and m regular functionfu f m the regular test functionf f m fu vanishes on the conjugacy classes in

the gan gross prasad conjecture for u n u n abstract we prove the gan gross prasad conjecture for u n u n under some local conditions using a relative trace formula we deduce some new cases of the gan gross prasad conjecture for u n 1 u n from the case of u n u n

preliminary study on recommended time duration of source signals to be analyzed in relation to its effective duration of the auto correlation function abstract a workable model of human auditory brain system including the auto correlation function acf and the interaural cross correlation function iacf has been reported 1 subjective evaluations can be described by physical factors extracted from both the acf of sound source and the iacf the purpose of this study is to find a recommended integration time 2 t r by using several noise and sound sources existing in an office results show the most suitable integration interval from the viewpoints of the loudness and the pitch can be determined in relation to the effective duration e of the sound source

spectral asymptotics for arithmetic quotients of sl n r so n in this article we study the asymptotic distribution of the cuspidal spectrum of arithmetic quotients of the symmetric space sl n r so n in particular we obtain weyl s law with an estimation on the remainder term this extends some of the main results of duistermaat kolk and varadarajan dkv1 to this setting

an automorphic generalization of the hermite minkowski theorem we show that for any integer n there are only finitely many cuspidal algebraic automorphic representations of rm gl n over mathbb q with n varying whose conductor is n and whose weights are in the interval 0 1 23 more generally we define a simple sequence r w w geq 0 such that for any integer w any number field e whose root discriminant is less than r w and any ideal n in the ring of integers of e there are only finitely many cuspidal algebraic automorphic representations of general linear groups over e whose conductor is n and whose weights are in the interval 0 1 w assuming a version of grh we also show that we may replace r w with 8 pi e gamma h w in this statement where gamma is euler s constant and h w the w th harmonic number the proofs are based on some new positivity properties of certain real quadratic forms which occur in the study of the weil explicit formula for rankin selberg l functions both the effectiveness and the optimality of the methods are discussed

compactlike discrete breathers in systems with nonlinear and nonlocal dispersive terms discrete breathers with purely anharmonic short range interaction potentials localize superexponentially becoming compactlike we analyze their spatial localization properties and their dynamical stability several branches of solutions are identified one of them connects to the well known page and sievers takeno lattice modes another one connects with the compacton solutions of rosenau the absence of linear dispersion allows for extremely long lived time quasiperiodic localized excitations adding long range anharmonic interactions leads to an extreme case of competition between length scales defining the spatial breather localization we show that short and long range interaction terms competition results in the appearance of several characteristic crossover lengths and essentially breaks the concept of compactness of the corresponding discrete breathers

discrete compactons some exact results in this letter we use the method of constructing exact solutions on lattices proposed by kinnersley and described in schmidt 1979 phys rev b 20 4397 to obtain exact compacton solutions in discrete models we examine the linear stability of such solutions both for the bright compacton and for the dark compacton cases we focus on a quantization condition that the width of the profile should satisfy we also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus the possibility of multi compacton solutions is considered

level raising and symmetric power functoriality iii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

applications of langlands functorial lift of odd orthogonal groups together with cogdell piatetski shapiro and shahidi we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of so 2n 1 to gl 2n recently ginzburg rallis and soudry obtained a more precise form of the lift using their integral representation technique namely the lift is an isobaric sum of cuspidal representations of gln i more precisely cuspidal representations of gl2n i such that the exterior square l functions have a pole at s 1 one purpose of this paper is to give a simpler proof of this fact in the case that a cuspidal representation has one supercuspidal component in a separate paper we prove it without any condition using a result on spherical unitary dual due to barbasch and moy we give several applications of the functorial lift first we parametrize square integrable representations with generic supercuspidal support which have been classified by moeglin and tadic second we give a criterion for cuspidal reducibility of supercuspidal representations of gl m x so 2n 1 third we obtain a functorial lift from generic cuspidal representations of so 5 to automorphic representations of gl 5 corresponding to the l group homomorphism sp 4 c gl 5 c given by the second fundamental weight

traveling wave solutions of the bbm like equations in this work we apply the factorization technique to the benjamin bona mahony like equations b m n in order to get traveling wave solutions we will focus on some special cases for which m n and we will obtain these solutions in terms of the special forms of weierstrass functions

even galois representations and the fontaine mazur conjecture we prove under mild hypotheses that there are no irreducible two dimensional ordinary even galois representations of mathrm gal overline mathbf q mathbf q with distinct hodge tate weights this is in accordance with the fontaine mazur conjecture if k q is an imaginary quadratic field we also prove again under certain hypotheses that mathrm gal overline mathbf q k does not admit irreducible two dimensional ordinary galois representations of non parallel weight

on twisted lifting if a is a generator of the galois group of a finite cyclic extension e f of local or global fields and e is a character of ce ex or ex ax whose restriction to cf has order n then the irreducible admissible or automorphic representations 1 cf denotes the multiplicative group fx if f is local and the idele class group fx a x if f is global put g gl and fix a character e of ce whose restriction to cf is of order n it determines a character e of g e or g e g ae by e g e det g the restriction of e to cf determines by class field theory a cyclic extension fe of f of degree n fix a generator a of the galois group gal e f denote by r g the set of equivalence classes of irreducible admissible or automorphic representations of g e or g ae then a acts on r g by v g vr a g g in g e or g a and we denote by re g the set of vr in r g with v n e theorem fftere ex s i a natural bijection between are g and the set of gal f f orbits of characters on nl fcl where l fee in the case e f this is due to kazhdan k in the local case and if it is cuspidal with two supercuspidal components kazhdan s proof is remarkably elegant com plete local and global results are derived from the study of the unramified case only our proof follows kazhdan s and uses kottwitz s base change lemma ko and arthur s explicit trace formula a we also show lemma 15 1 that the above 77 are induced ip r from a representation t t t e t e v e where e e 1 and t is a super cuspidal representation of gl w e n mm f is a parabolic subgroup with levi component gl m m then if l e n fe is an extension of f of degree we must have that divides m corollary 16 2 and m l is prime to e proposition 17 1 for example in the special case where e fe each it of the above type is induced from a character of a borel subgroup hence it is not in the discrete series we proved this result in f when e fe is a quadratic extension of f using the trace formula twisted as here in fact this motivated us to look for a twisted analogue of kazhdan s lifting further description of our vr is given in 16 and 17

the formation of the dead core in parabolic reaction diffusion problems on donne des conditions pour l existence d une region a concentration de reactant nulle pour des problemes paraboliques non lineaires de reaction diffusion

on the symmetric square applications of a trace formula in this paper we prove the existence of the symmetric square lifting of admissible and of automorphic representations from the group sl 2 to the group pgl 3 complete local results are obtained relating the character of an sl 2 packet with the twisted character of self contragredient pgl 3 modules our global results relate packets of cuspidal representations of sl 2 with a square integrable component and self contragredient automorphic pgl 3 modules with a component coming from a square integrable one the sharp results which concern sl 2 rather than gl 2 are afforded by the usage of the trace formula the surjectivity and injectivity of the correspondence implies that any self contragredient automorphic pgl 3 module as above is a lift and that the space of cuspidal sl 2 modules with a square integrable component admits multiplicity one theorem and rigidity strong multiplicity one theorem for packets and not for individual representations

sato tate theorem for families and low lying zeros of automorphic l functions we consider certain families of automorphic representations over number fields arising from the principle of functoriality of langlands let g be a reductive group over a number field f which admits discrete series representations at infinity let l g widehat g rtimes mathrm gal bar f f be the associated l group and r l g rightarrow mathrm gl d mathbb c a continuous homomorphism which is irreducible and does not factor through mathrm gal bar f f the families under consideration consist of discrete automorphic representations of g mathbb a f of given weight and level and we let either the weight or the level grow to infinity we establish a quantitative plancherel and a quantitative sato tate equidistribution theorem for the satake parameters of these families this generalizes earlier results in the subject notably of sarnak prog math 70 321 331 1987 and serre j am math soc 10 1 75 102 1997 as an application we study the distribution of the low lying zeros of the associated family of l functions l s pi r assuming from the principle of functoriality that these l functions are automorphic we find that the distribution of the 1 level densities coincides with the distribution of the 1 level densities of eigenvalues of one of the unitary symplectic and orthogonal ensembles in accordance with the katz sarnak heuristics we provide a criterion based on the frobenius schur indicator to determine this symmetry type if r is not isomorphic to its dual r vee then the symmetry type is unitary otherwise there is a bilinear form on mathbb c d which realizes the isomorphism between r and r vee if the bilinear form is symmetric resp alternating then r is real resp quaternionic and the symmetry type is symplectic resp orthogonal

an example of non normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type due to the work of arthur and clozel ac the automorphic induction for cyclic galois extensions of prime degree is well understood in great generality it is not the case for non normal extensions even for monomial representations i e the ones induced from grossencharacters the only examples we have at the moment are first non normal cubic automorphic induction due to jacquet piatetski shapiro and shalika jpss they obtained the automorphic induction as a consequence of the converse theorem on gl3 the second example is that of harris h he constructed automorphic induction for special class of algebraic hecke characters of suitable non normal extensions with solvable galois closure in this note we give an example of automorphic induction for nonnormal quintic extension whose galois closure is not solvable theorem 6 3 in fact the galois group is a5 the alternating group on 5 letters the key observation due to ramakrishnan is that symmetric fourth of the two dimensional icosahedral representation is equivalent to a suitable twist by a character of the five dimensional monomial representation of a5 our result follows immediately by combining results of k buzzard m dickinson n shepherd barron and r taylor bdst or r taylor s result ta2 on modularity of certain icosahedral representations and our result on the functoriality of symmetric fourth ki we also prove the modularity of all symmetric powers of cuspidal representations of icosahedral type theorem 6 4

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

the running autocorrelation function of different music signals relating to preferred temporal parameters of sound fields this paper defines the minimum value of the effective duration of the running autocorrelation function of a music signal used in subjective preference testing a short duration signal which may relate to psychological present is more suitable for calculating the most preferred time delay of the single reflection than is the long time autocorrelation function this fact is found particularly when passages of japanese music are being played which include a wide range noise component at the very beginning of the signal and the so called ma ma is a stationary sound passage without any rapid movement this paper also shows that for subsequent reverberation time a flat frequency response may be in the range of preferred conditions such preferred conditions may be calculated by the minimum effective duration of the running autocorrelation function of source signals after passing through the a weighting network

the artin conjecture for some s_5 extensions we establish some new cases of artin s conjecture our results apply to galois representations over mathbf q with image s 5 satisfying certain local hypotheses the most important of which is that complex conjugation is conjugate to 12 34 in fact we prove the stronger claim conjectured by langlands that these representations are automorphic for the irreducible representations of dimensions 4 and 6 our result follows from known 2 dimensional cases of artin s conjecture proved by sasaki as well as the functorial properties of the asai transfer proved by ramakrishnan for the irreducible representations of dimension 5 we encounter the problem of descending an automorphic form from a quadratic extension compatibly with the galois representation this problem is partly solved by working instead with a four dimensional representation of some central extension of s 5 our modularity results in this case are contingent on the non vanishing of a certain dedekind zeta function on the real line in the critical strip a result of booker show that one can in principle explicitly verify this non vanishing and with booker s help we give an example verifying artin s conjecture for representations coming from the galois closure of the quintic field k of smallest discriminant 1609

a converse theorem for gl n we complete the work of cogdell and piatetski shapiro 3 to prove for n 3 a converse theorem for automorphic representations of gln over a number field with analytic data from twists by unramified representations of gln 1

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

unitary quasi lifting applications let tj 3 be the quasi split unitary group in three variables defined using a quadratic extension e f of number fields complete local and global results are obtained for the o endo unstable lifting from u 2 to gl 3 e this is used to establish quasi endo lifting for automorphic forms from u 2 to u 3 by means of base change from uf3 to gl 3 e base change quasi lifting is also proven continuing the work of i the exposition is elementary and uses only a simple form of an identity of trace formulas and base change transfer of orbital integrals of spherical functions

strong multiplicity theorems for let 7r 7rv be a cuspidal automorphic representation of gl n fa where fa denotes the adeles of a number field f let e be a galois extension of f and let g denote a conjugacy class of the galois group the author considers those cuspidal automorphic representations which have local components 7rv whenever the frobenius of the prime v is 9 showing that such representations are often easily described and finite in number this generalizes a result of moreno bull amer math soc 11 1984 pp 180 182 1 notation we first introduce the notation to be used throughout this paper let fa denote the ring of adeles of a number field f we denote by v a typical prime of f usually finite and by fv the completion of f at v when v is finite we write nv for the order of its residue field an automorphic cuspidal representation of gl n fa denoted by 7r is an irreducible component of the right regular representation of gl n fa on the space of automorphic cuspidal forms for the definition of an automorphic form see 1 19 we write ir for the contragredient representation to 7r the representation 7r factors into a product of local representations 7r 7rv those local representations whose restriction to the maximal compact subgroup of gl n fv contains the trivial representation are said to be unramified attached to 7r is a global l function l s 7r which is a product of local l functions lv s 7rv which for finite unramified primes are of the form n lv s 7rv 1 hv inv 8 l i l the complex numbers uv i are called eigenvalues of 7rv for finite unramified primes the central character of 7r at v is just t q 1 pv i 7 we remark that if x is a unitary character of the ideles of f then 7r x x 7r x xodet

on the images of modular and geometric three dimensional galois representations we study compatible families of three dimensional galois representations constructed in the etale cohomology of a smooth projective variety we prove a theorem asserting that the residual images will be generically large if certain easy to check conditions are satisfied we only consider representations with coefficients in an imaginary quadratic field for primes inert in this field the residual representations when irreducible are unitary we apply our result to an example constructed by van geemen and top obtaining a family of special linear groups and one of special unitary groups as galois groups over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we also consider the case of cohomological modular forms for a congruence subgroup of sl inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i assuming clozel s conjecture stating that a geometric family of three dimensional galois representations can be attached to them we verify for three examples the conditions guaranteeing generically large images and explicitly bound the finite set of primes with non maximal image we also discuss what intrinsic conditions a modular form should verify to guarantee that the images of the attached galois representations will be generically large

subjective preference for sound sources located on the stage and in the orchestra pit of an opera house abstract the present study investigates whether the subjective preference theory can be applied to the sound field in an opera house paired comparison tests were conducted to obtain scale values of subjective preference as the source locations of the music on the stage and in the orchestra pit were moved listeners were asked to give their acoustical preference the acoustical factors at each listening position were obtained from the interaural cross correlation function and binaural impulse responses measured at each listening position the relationship between the scale values of subjective preference and orthogonal acoustical factors ll iacc iacc t1 for the pit source t1 for the stage tsub for the pit source and tsub for the stage source was determined by using factor analysis which shows that the preference theory is applicable total scores obtained from factor analysis and measured scale values are in good agreement

a diagnostic system measuring orthogonal factors of sound fields in a scale model of auditorium abstract based on the model of auditory brain system which consists of the autocorrelation mechanism the interaural cross correlation mechanism between both the auditory pathways and the specialization of human cerebral hemispheres y ando 1998 architectural acoustics blending sound sources sound fields and listeners new york aip press springer verlag a new diagnostic system was developed after obtaining the binaural impulse response four orthogonal factors including the spl the initial time delay gap between the direct sound and the first reflection the subsequent reverberation time and the iacc can be analyzed for the calculation of the scale values of both global and individual subjective preferences in addition two more factors extracted from the interaural cross correlation function iacc and wiacc can be figured out also the sound energy 0 the effective duration e and fine structures of autocorrelation function of sound signals including the magnitude of first maximum 1 and its delay time 1 can be analyzed as an example of the measurement effects of reflectors array above the stage in a 1 10 scale model of auditorium at each seat are discussed here

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

potential automorphy and change of weight we prove an automorphy lifting theorem for l adic representations where we impose a new condition at l which we call potentential diagonalizability this result allows for change of weight and seems to be substantially more exible than previous theorems along the same lines we derive several applications for instance we show that any irreducible totally odd essentially self dual regular weakly compatible system of l adic representations of the absolute galois group of a totally real eld is potentially automorphic and hence is pure and its l function has meromorphic continuation to the whole complex plane and satises the expected functional equation

geometrical parameter combinations that correlate with early interaural cross correlation coefficients in a performance hall the previous binaural data of the authors measured inside two multi purpose performance halls are re analyzed using regression in this study it is done in an attempt to establish a framework that can improve the prediction of early interaural cross correlation coefficients iaccs but with as little measurement effort and parameters as possible the results show that regression models consist of linear combinations of polynomials of geometrical parameters when used together with the measurement schemes suggested previously by the authors are sufficient for predicting the iaccs to within engineering tolerance the predictions are better than those obtained previously by the neural network approach of the authors the relative importance of the geometrical parameters in the prediction of iaccs is also investigated

super exponential decay and holomorphic extensions for semilinear equations with polynomial coefficients abstract we show that all eigenfunctions of linear partial differential operators in r n with polynomial coefficients of shubin type are extended to entire functions in c n of finite exponential type 2 and decay like exp z 2 for z in conic neighbourhoods of the form im z re z we also show that under semilinear polynomial perturbations all nonzero homoclinics keep the super exponential decay of the above type whereas a loss of the holomorphicity occurs namely we show holomorphic extension into a strip z c n im z t for some t 0 the proofs are based on geometrical and perturbative methods in gelfand shilov spaces the results apply in particular to semilinear schrodinger equations of the form u x 2 u u f x u u our estimates on homoclinics are sharp in fact we exhibit examples of solutions of with super exponential decay which are meromorphic functions the key point of our argument being the celebrated great picard theorem in complex analysis