boundedness of automorphic l functions in vertical strips the purpose of this paper is to prove the boundedness in vertical strips of finite width for all the l functions that appear in constant terms of eisenstein series under a certain natural assumption on local normalized intertwining operators as a corollary we prove the boundedness for a number of important l functions among them the symmetic cube and triple product l functions attached to cusp forms on gl 2 as well as several rankin selberg product l functions where the local assumption was alredy proved to be valid in each case under the same assumption the finiteness of poles on all of c for all of these l functions is also proved a necessary step in the proof of boundedness in vertical strips

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

harmonics to noise ratio as an index of the degree of hoarseness degree of hoarseness can be evaluated by judging the extent to which noise replaces the harmonic structure in the spectrogram of a sustained vowel however this visual method is subjective the present study was undertaken to develop the harmonics to noise h n ratio as an objective and quantitative evaluation of the degree of hoarseness the computation is conceptually straightforward 50 consecutive pitch periods of a sustained vowel a are averaged h is the energy of the averaged waveform while n is the mean energy of the differences between the individual periods and the averaged waveform recordings of 42 normal voices and 41 samples with varying degrees of hoarseness were analyzed two experts rated the spectrogram of each voice sample based on the amount of noise relative to that of the harmonic component the results showed a highly significant agreement the rank correlation coefficient 0 849 between h n calculations and the subjective evaluations of the spectrograms the h n ratio also proved useful in quantitatively assessing the results of treatment for hoarseness

euler systems for rankin selberg convolutions of modular forms we construct a euler system in the cohomology of the tensor product of the galois representations attached to two modular forms using elements in the higher chow groups of products of modular curves we use these elements to prove a finiteness theorem for the strict selmer group of the galois representation when the associated p adic rankin selberg l function is nonvanishing at s 1

perturbation free measurement of the harmonics to noise ratio in voice signals using pitch synchronous harmonic analysis the measurement of the harmonics to noise ratio hnr in speech signals gives an indication of the aperiodicity of the speech waveform this may be due to the presence of jitter shimmer additive noise waveshape change or some unknown combination of these factors in order to estimate the hnr as a measure of the additive noise component only the contaminating effects of the other contributory components must first be removed a pitch synchronous harmonic analysis is proposed to overcome this problem the procedure takes advantage of the time scale compression frequency expansion property of the fourier series in order to eliminate jitter and shimmer successive spectra are added by harmonic number as opposed to frequency location and perturbation is removed due to the fact that the relative heights of the harmonic components remain the same for scaled signals the technique is examined on synthetically generated voice signals a discussion of the results is given in terms of human voice signals characterization of jitter vocal tract filtering effects perturbation mechanisms nonlinear dynamics and the possibility of developing the method for use with inverse filtering strategies

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

cuspidality of symmetric powers with applications the purpose of this paper is to prove that the symmetric fourth power of a cusp form on rm gl 2 whose existence was proved earlier by the first author is cuspidal unless the corresponding automorphic representation is of dihedral tetrahedral or octahedral type as a consequence we prove a number of results toward the ramanujan petersson and sato tate conjectures in particular we establish the bound q sp 1 9 sb v for unramified hecke eigenvalues of cusp forms on rm gl 2 over an arbitrary number field this is the best bound available at present

spectral characterization of jitter shimmer and additive noise in synthetically generated voice signals alteration of the harmonic structure in voice source spectra taken over at least two periods of the waveform may occur due to the presence of fundamental frequency f0 perturbation amplitude perturbation additive noise or changes within the glottal source signal itself in order to make accurate inferences regarding glottal flow dynamics or perceptual evaluations based on spectral measurements taken from the acoustic speech waveform investigation of the spectral features of each aperiodic component is required based on a heuristic development involving a consideration of the partial sum of the fourier series taken for two periods of a jittered shimmered and additive random noise contaminated signal the corresponding spectral characteristics are hypothesized subsequent to this the fourier series coefficients are calculated for the two periods in order to test the hypotheses definite spectral differences are found for each aperiodic component based on these findings differential quantitative spectral measurements are suggested further supportive evidence is obtained through use of fourier transform and periodogram averaged calculations the analysis is carried out on synthetically generated glottal pulse waveforms and on radiated speech waveforms a discussion of the results is given in terms of voice aperiodicity in general and in terms of their implication for future studies involving human voice signals

relating invariant linear form and local epsilon factors via global methods we use the recent proof of jacquet s conjecture due to harris and kudla hk and the burger sarnak principle see bs to give a proof of the relationship between the existence of trilinear forms on representations of gl 2 k u for a non archimedean local field k u and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in p1 theorem 1 4 the method used is very flexible and gives a global proof of a theorem of saito and tunnell about characters of gl 2 using a theorem of waldspurger w theorem 2 about period integrals for gl 2 and also an extension of the theorem of saito and tunnell by this author in p3 theorem 1 2 which was earlier proved only in odd residue characteristic in the appendix to this article h saito gives a local proof of lemma 4 which plays an important role in the article

mixing logics and rewards for the component oriented specification of performance measures formal notations for system performance modeling need to be equipped with suitable notations for specifying performance measures these companion notations have been traditionally based on reward structures and more recently on temporal logics in this paper we propose an approach that combines logics and rewards together with a definition mechanism that allows performance measures to be specified in a component oriented way thus facilitating the task for non experts the resulting measure specification language msl is interpreted both on action labeled continuous time markov chains and on stochastic process algebras the latter interpretation provides a compositional framework for performance sensitive model manipulations and emphasizes the increased expressiveness with respect to traditional reward structures for implicit state modeling notations

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

universal eigenvarieties trianguline galois representations and p adic langlands functoriality using the overconvergent cohomology modules introduced by ash and stevens we construct eigenvarieties associated with reductive groups and establish some basic geometric properties of these spaces building on work of ash stevens urban and others we also formulate a precise modularity conjecture linking trianguline galois representations with overconvergent cohomology classes in the course of giving evidence for this conjecture we establish several new instances of p adic langlands functoriality our main technical innovations are a family of universal coefficients spectral sequences for overconvergent cohomology and a generalization of chenevier s interpolation theorem

concerning the lp norm of spectral clusters for second order elliptic operators on compact manifolds in this paper we study the lp l2 mapping properties of a spectral projection operator for riemannian manifolds this operator is a generalization of the harmonic projection operator for spherical harmonics on s see c d sogge duke math j 53 1986 43 65 among other things we generalize the l2 restriction theorems of c fefferman e m stein and p tomas bull amer math sot 81 1975 477478 for the fourier transform in r to the setting of riemannian manifolds we obtain these results for the spectral projection operator as a corollary of a certain sobolev inequality involving d r2 for large r this sobolev inequality generalizes certain results for r of c kenig a ruiz and the author duke math j 55 1987 329 347 the main tools in the proof of the sobolev inequalities for riemannian manifolds are the hadamard parametrix cf l hbrmander acta mad 88 1968 341 370 and the analysis of linear partial differential equations vol iii springer verlag new york 1985 and oscillatory integral theorems of l carleson and p sjolin studia math 44 19x 287 299 and stein arm math stud 112 1986 307 357 0 1988 academic pnss iw

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

the role of the ramanujan conjecture in analytic number theory we discuss progress towards the ramanujan conjecture for the group gln and its relation to various other topics in analytic number theory

quadratic forms representing all odd positive integers we consider the problem of classifying all positive definite integer valued quadratic forms that represent all positive odd integers kaplansky considered this problem for ternary forms giving a list of 23 candidates and proving that 19 of those represent all positive odds jagy later dealt with a 20th candidate assuming that the remaining three forms represent all positive odds we prove that an arbitrary positive definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451 this result is analogous to bhargava and hanke s celebrated 290 theorem in addition we prove that these three remaining ternaries represent all positive odd integers assuming the generalized riemann hypothesis this result is made possible by a new analytic method for bounding the cusp constants of integer valued quaternary quadratic forms q with fundamental discriminant this method is based on the analytic properties of rankin selberg l functions and we use it to prove that if q is a quaternary form with fundamental discriminant the largest locally represented integer n for which q vec x n has no integer solutions is o d 2 epsilon

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

galois representations with quaternion multiplication associated to noncongruence modular forms in this paper we study the compatible family of degree 4 scholl representations associated with a space s of weight 2 noncongruence cusp forms satisfying quaternion mul tiplications over a biquadratic extension of q it is shown that is automorphic that is its associated l function has the same euler factors as the l function of an automorphic form for gl4 over q further it yields a relation between the fourier coefficients of noncongruence cusp forms in s and those of certain automorphic forms via the three term atkin and swinnerton dyer congruences

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

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

composition and behaviors of probabilistic i o automata abstract we augment the i o automaton model of lynch and tuttle with probability as a step toward the ultimate goal of obtaining a useful tool for specifying and reasoning about asynchronous probabilistic systems our new model called probabilistic i o automata preserves the fundamental properties of the i o automaton model such as the asymmetric treatment of input and output and the pleasant notion of asynchronous composition for certain classes of probabilistic i o automata we show that probabilistic behavior maps which are an abstract representation of i o automaton behavior in terms of a certain expectation operator are compositional and fully abstract with respect to a natural notion of probabilistic testing

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

on the sl 2 period integral let e f be a quadratic extension of number fields for a cuspidal representation of sl2 ae we study in this paper the integral of functions in on sl2 f sl2 af we characterize the nonvanishing of these integrals called period integrals in terms of having a whittaker model with respect to characters of e ae which are trivial on af we show that the period integral in general is not a product of local invariant functionals and find a necessary and sufficient condition when it is we exhibit cuspidal representations of sl2 ae whose period integral vanishes identically while each local constituent admits an sl2 invariant linear functional finally we construct an automorphic representation on sl2 ae which is abstractly sl2 af distinguished but for which none of the elements in the global l packet determined by it is distinguished by sl2 af

the residual eisenstein cohomology of sp_ 4 over a totally real number field let g sp4 k be the k split symplectic group of k rank 2 where k is a totally real numbereld in this paper we compute the eisenstein cohomology of g with respect to anynite dimensional irreducible k rational representation e of g1 rk qg r where rk q denotes the restriction of scalars from k to q the approach is based on the work of schwermer regarding the eisenstein cohomology for sp4 q kim s description of the residual spectrum of sp4 and the frankeltration of the space of automorphic forms in fact taking the representation theoretic point of view we write for the group g the frankeltration with respect to the cuspidal support and give a precise description of theltration quotients in terms of induced representations this is then used as a prerequisite for the explicit computation of the eisenstein cohomology the special focus is on the residual eisenstein cohomology under a certain compatibility condition for the coefficient system e and the cuspidal support we prove the existence of non trivial residual eisenstein cohomology classes which are not square integrabl e that is represented by a non square integrabl residue of an eisenstein series

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

emergent spacetime from modular motives the program of constructing spacetime geometry from string theoretic modular forms is extended to calabi yau varieties of dimensions three and four as well as higher rank motives modular forms on the worldsheet can be constructed from the geometry of spacetime by computing the l functions associated to omega motives of calabi yau varieties generated by their holomorphic n forms via galois representations the modular forms that emerge in this way are related to characters of the underlying rational conformal field theory the converse problem of constructing space from string theory proceeds in the class of diagonal theories by determining the motives associated to modular forms in the category of pure motives with complex multiplication the emerging picture suggests that the l function can be viewed as defining a map between the geometric category of motives and the category of conformal field theories on the worldsheet

weak subconvexity without a ramanujan hypothesis we describe a new method to obtain weak subconvexity bounds for l functions with mild hypotheses on the size of the dirichlet coefficients we verify these hypotheses for all automorphic l functions and with mild restrictions the rankin selberg l functions attached to two automorphic representations the proof relies on a new unconditional log free zero density estimate for rankin selberg l functions

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

generalised form of a conjecture of jacquet and a local consequence following the work of harris and kudla we prove a general form of a conjecture of jacquet relating the non vanishing of a certain period integral to non vanishing of the central critical value of a certain l function as a consequence we deduce a theorem relating the existence of gl 2 k invariant linear forms on irreducible admissible representations of gl 2 k for a commutative semi simple cubic algebra k over a non archimedean local field k in terms of local epsilon factors which was proved only in some cases by the first author in his earlier work in d prasad invariant forms for representations of gl 2 over a local field amer j math 114 1992 no 6 1317 1363 this has been achieved by globalising a locally distinguished supercuspidal representation to a globally distinguished representation a result of independent interest which is proved by an application of the relative trace formula

modularity of the rankin selberg l series and multiplicity one for sl 2 let f g be primitive cusp forms holomorphic or otherwise on the upper half plane h of levels n m respectively with unitarily normalized l functions l s f equation and l s g equation when p does not divide n resp m the inverse roots p p resp p p are nonzero with sum ap resp bp for every p prime to nm set lp s f g 1 p pp s 1 p pp s 1 p pp s 1 p pp s 1 let l s f g denote the incomplete euler product of lp s f g over all p not dividing nm this is closely related to the convolution l series sum over n 1 a sub n b sub n n s whose miraculous properties were first studied by rankin and selberg

on shalika periods and a theorem of jacquet martin let pi be a cuspidal automorphic representation of gl 4 bbb a with central character mu 2 it is known that pi has shalika period with respect to mu if and only if the l function l s s pi bigwedge 2 otimes mu 1 has a pole at s 1 jacquet and martin considered the analogous question for cuspidal representations pi d of the inner form gl 2 d bbb a and obtained a partial result via the relative trace formula in this paper we provide a complete solution to this problem via the method of theta correspondence and give necessary and sufficient conditions for the existence of shalika period for pi d we also resolve the analogous question in the local setting

a miyawaki type lift for textit gspin 2 10 let mathfrak t 2 resp mathfrak t be the hermitian symmetric domain of textit spin 2 10 resp e 7 3 in previous work compos math 152 2 223 254 2016 we constructed holomorphic cusp forms on mathfrak t from elliptic cusp forms with respect to textit sl 2 mathbb z by using such cusp forms we construct holomorphic cusp forms on mathfrak t 2 which are similar to miyawaki lift constructed by ikeda duke math j 131 469 497 2006 in the context of symplectic groups it is conditional on the conjectural jacquet langlands correspondence from textit pgso 2 10 to textit pgso 6 6

a 2 adic automorphy lifting theorem for unitary groups over cm fields we prove a minimal type automorphy lifting theorem for 2 adic galois representations of unitary type over imaginary cm fields we use this to improve an automorphy lifting theorem of kisin for mathrm gl 2

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points ii we prove a general subconvex bound in the level aspect for rankin selberg l functions associated with two primitive holomorphic or maass cusp forms over q we use this bound to establish the equidistribution of incomplete galois orbits of heegner points on shimura curves associated with indefinite quaternion algebras over q

darmon points on elliptic curves over number fields of arbitrary signature we present new constructions of complex and pp adic darmon points on elliptic curves over base fields of arbitrary signature we conjecture that these points are global and present numerical evidence to support our conjecture

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

temporal and spectral estimations of harmonics to noise ratio in human voice signals the quantity harmonic to noise ratio hnr has been used to estimate the level of noise in human voice signals hnr estimation can be accomplished in two ways 1 on a time domain basis in which hnr is computed directly from the acoustic waveform and 2 on a frequency domain basis in which hnr is computed from a transformed representation of the waveform an algorithm for computing hnr in the frequency domain was modified and tested in the work described here the modifications were designed to reduce the influence of spectral leakage in the computation of harmonic energy and to remove the necessity of spectral baseline shifting prescribed in one existing algorithm g de krom j speech hear res 36 254 266 1993 frequency domain estimations of hnr based on this existing algorithm and our modified algorithm were compared to time domain estimations on synthetic signals and human pathological voice samples results indicated a highly significant linear correlation between frequency and time domain estimations of hnr for our modified approach

a note on maass forms of icosahedral type using ideas of ramakrishnan we consider the icosahedral analogue of the theorems of sarnak and brumley on hecke maass newforms with fourier coefficients in a quadratic order although we are unable to conclude the existence of an associated galois representation in this case we show that one can deduce some implications of such an association including weak automorphy of all symmetric powers and the value distribution of fourier coefficients predicted by the chebotarev density theorem

the local langlands conjecture for gsp 4 ii the case of inner forms in an earlier paper of the first author and shuichiro takeda the local langlands correspondence for rm gsp 4 f over a non archimedean local field f of characteristic zero was established and several expected properties of the correspondence verified in this paper we extend the local langlands correspondence to the inner form rm gu 2 d of rm gsp 4

the effect of convolving families of l functions on the underlying group symmetries let fn and gm be families of primitive automorphic l functions for gln aq and glm aq respectively such that as n m the statistical behavior 1 level density of the low lying zeros of l functions in fn resp gm agrees with that of the eigenvalues near 1 of matrices in g1 resp g2 as the size of the matrices tend to infinity where each gi is one of the classical compact groups unitary u symplectic sp or orthogonal o so even so odd assuming that the convolved families of l functions fn gm are automorphic we study their 1 level density we also study convolved families of the form f gm for a fixed f under natural assumptions on the families which hold in many cases we can associate to each family l of l functions a symmetry constant cl equal to 0 resp 1 or 1 if the corresponding low lying zero statistics agree with those of the unitary resp symplectic or orthogonal group our main result is that cf g cf cg the symmetry type of the convolved family is the product of the symmetry types of the two families a similar statement holds for the convolved families f gm we provide examples built from dirichlet l functions and holomorphic modular forms and their symmetric powers an interesting special case is to convolve two families of elliptic curves with positive rank in this case the symmetry group of the convolution is independent of the ranks in accordance with the general principle of multiplicativity of the symmetry constants but the ranks persist before taking the limit n m as lower order terms

further refinement of strong multiplicity one for gl 2 we obtain a sharp refinement of the strong multiplicity one theorem for the case of unitary non dihedral cuspidal automorphic representations for gl 2 given two unitary cuspidal automorphic representations for gl 2 that are not twist equivalent we also find sharp lower bounds for the number of places where the hecke eigenvalues are not equal for both the general and non dihedral cases we then construct examples to demonstrate that these results are sharp

a pitch synchronous analysis of hoarseness in running speech a method of pitch synchronous acoustic analysis of hoarseness requiring a voice sample of only four fundamental periods is presented this method calculates a noise to signal n s ratio which indicates the depth of valleys between harmonic peaks in the power spectrum the spectrum is calculated pitch synchronously from a fourier transform of the signal windowed through a continuously variable hanning window spanning exactly four fundamental periods a two stage procedure is used to determine the exact duration of the four fundamental periods an initial estimate is obtained using autocorrelation in the time domain a more precise estimate is obtained in the frequency domain by minimizing the errors between the preliminary calculated power spectrum and the predicted spectrum spread of a windowed harmonic signal analysis of synthesized voices showed that the n s ratio is sensitive to additive noise jitter and shimmer and is insensitive to slow 8 hz modulation in fundamental frequency and amplitude an analysis of pre and postoperative voices of six patients with benign laryngeal disease showed that the n s ratio for vowel u in running speech consistently improved after surgery for all subjects in agreement with their successful therapeutic results

performance measure sensitive congruences for markovian process algebras the modeling and analysis experience with process algebras has shown the necessity of extending them with priority probabilistic internal external choice and time while preserving compositionality the purpose of this paper is to make a further step by introducing a way to express performance measures in order to allow the modeler to capture the qos metrics of interest we show that the standard technique of expressing stationary and transient performance measures as weighted sums of state probabilities and transition frequencies can be imported in the process algebra framework technically speaking if we denote by n n the number of performance measures of interest in this paper we define a family of extended markovian process algebras with generative master reactive slaves synchronization mechanism called empagrn including probabilities priorities exponentially distributed durations and sequences of rewards of length n then we show that the markovian bisimulation equivalence mbn is a congruence for empagrn which preserves the specified performance measures and we give a sound and complete axiomatization for finite empagrn terms finally we present a case study conducted with the software tool two towers in which we contrast the average performance of a selection of distributed algorithms for mutual exclusion modeled with empagrn