weakly lefschetz symplectic manifolds for a symplectic manifold the harmonic cohomology of symplectic divisors introduced by donaldson 1996 and of the more general symplectic zero loci introduced by auroux 1997 are compared with that of its ambient space we also study symplectic manifolds satisfying a weakly lefschetz property that is the s lefschetz property in particular we consider the symplectic blow ups cp m of the complex projective space cp m along weakly lefschetz symplectic submanifolds m cp m as an application we construct for each even integer s 2 compact symplectic manifolds which are s lefschetz but not s 1 lefschetz

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations abstract we consider elliptic operators associated with discrete groups of quantized canonical transformations in order to be able to apply results from algebraic index theory we define the localized algebraic index of the complete symbol of an elliptic operator with the help of a calculus of semiclassical quantized canonical transformations a version of egorov s theorem and a theorem on trace asymptotics for semiclassical fourier integral operators we show that the localized analytic index and the localized algebraic index coincide as a corollary we express the fredholm index in terms of the algebraic index for a wide class of groups in particular for finite extensions of abelian groups

pullbacks of saito kurokawa lifts pullbacks of siegel eisenstein series have been studied by garrett 17 18 bocherer 6 7 heim 26 and play a key role in the proof of the algebraicity of critical values of certain automorphic l functions more generally one might consider pullbacks of siegel cusp forms for example ikeda 30 gave a conjectural formula for pullbacks of ikeda lifts 29 in terms of critical values of l functions for spn gl2 also the gross prasad conjecture 22 23 8 27 8 would relate pullbacks of siegel cusp forms of degree 2 to central critical values of l functions for gsp2 gl2 gl2 indeed bocherer furusawa and schulze pillot 8 gave an explicit formula for pullbacks of yoshida lifts 57 in this paper we give an explicit formula for pullbacks of saito kurokawa lifts and prove the algebraicity of central critical values of certain l functions for sp1 gl2 to be precise let be an odd positive integer let f s2 sl2 z be a normalized hecke eigenform and h s 1 2 0 4 a hecke eigenform associated to f by the shimura correspondence let f s 1 sp2 z be the saito kurokawa lift of h for each normalized hecke eigenform g s 1 sl2 z we consider the period integral f h h g g given by f h h g g

on mod p properties of siegel modular forms we prove two results on mod p properties of siegel modular forms first we use theta series in order to construct of a siegel modular form of weight p 1 which is congruent to 1 mod p second we define a theta operator vartheta on q expansions and show that the algebra of siegel modular forms mod p is stable under vartheta by exploiting the relation between vartheta and generalized rankin cohen brackets

on the holomorphic differential forms of the siegel modular variety ii in this paper we follow our investigation about the construction of alternating differential forms on the siegel s modular variety let a represent the quotient of the siegel s upper half space hg by the full integral symplectic group sp 29 z fg it is a well known fact that ag is a quasi projective algebraic variety we shall denote by 4g its satake s compactification it is a normal projective but singular variety we shall denote by a0 the regular part of ag and by t 0 a desingularization of ag without loss of generality we can assume ao contained in ao for any complex manifold m we shall denote by or m the sections of the sheaf of alternating holomorphic differential forms on m of degree v in 3 it has been shown that for g 2 the injection

a cochlear frequency position function for several species 29 years later accurate cochlear frequency position functions based on physiological data would facilitate the interpretation of physiological and psychoacoustic data within and across species such functions might aid in developing cochlear models and cochlear coordinates could provide potentially useful spectral transforms of speech and other acoustic signals in 1961 an almost exponential function was developed greenwood 1961b 1974 by integrating an exponential function fitted to a subset of frequency resolution integration estimates critical bandwidths the resulting frequency position function was found to fit cochlear observations on human cadaver ears quite well and with changes of constants those on elephant cow guinea pig rat mouse and chicken bekesy 1960 as well as in vivo behavioral anatomical data on cats schucknecht 1953 since 1961 new mechanical and other physiological data have appeared on the human cat guinea pig chinchilla monkey and gerbil it is shown here that the newer extended data on human cadaver ears and from living animal preparations are quite well fit by the same basic function the function essentially requires only empirical adjustment of a single parameter to set an upper frequency limit while a slope parameter can be left constant if cochlear partition length is normalized to 1 or scaled if distance is specified in physical units constancy of slope and form in dead and living ears and across species increases the probability that the function fitting human cadaver data may apply as well to the living human ear this prospect increases the function s value in plotting auditory data and in modeling concerned with speech and other bioacoustic signals since it fits the available physiological data well and consequently if those data are correct remains independent of and an appropriate means to examine psychoacoustic data and assumptions

cochlear generation of intermodulation distortion revealed by dpoae frequency functions in normal and impaired ears distortion product otoacoustic emission dpoae frequency functions were measured in normal hearing and hearing impaired ears a fixed f2 swept f1 paradigm was used with f2 fixed at half octave intervals from 1 to 8 khz l1 was always 10 db greater than l2 and l2 was varied from 65 to 10 db spl in 5 db steps the responses were quantified by the frequency and amplitude of the peak response peak responses were closer to f2 in higher frequency regions and for lower intensity stimulation results from hearing impaired subjects suggest that audiometric thresholds at the distortion product frequency fdp in addition to hearing status at f2 can affect dpoae results results are discussed in terms of several manifestations of a second resonance model as well as a dual source model for the generation of dpoaes as measured in the ear canal of humans it appears that a dual source model accounts for the data better than second filter models

equivariant lefschetz number of differential operators let g be a compact lie group acting on a compact complex manifold m by holomorphic transformations we prove a trace density formula for the g lefschetz number of a holomorphic differential operator on m we generalize the recent results of engeli and the first author to orbifolds

the modular variety of hyperelliptic curves of genus three the modular variety of nonsingular and complete hyperelliptic curves with level two structure of genus 3 is a 5 dimensional quasi projective variety which admits several standard compactifications the first one realizes this variety as a subvariety of the siegel modular variety of level two and genus three it has 36 irreducible isomorphic components one of the purposes of this paper will be to describe the equations of one of these components two further models use the fact that hyperelliptic curves of genus three can be obtained as coverings of a projective line with 8 branch points there are two important compactifications of this configuration space the first one y uses the semistable degenerated point configurations in p 1 8 this variety also can be identified with a baily borel compactified ball quotient y b 1 i we will describe these results in some detail and obtain new proofs including some finer results for them the other compactification uses the fact that families of marked projective lines can degenerate to stable marked curves of genus 0 we use the standard notation m 0 8 for this compactification we have a diagram the horizontal arrow is only birational but not everywhere regular in this paper we find another realization of this triangle which uses the fact that there are graded algebras closely related to algebras of modular forms a b such that x proj a y proj b

on the lifting of elliptic cusp forms to siegel cusp forms of degree 2n i 1 cf 8 in this paper we will prove that their conjecture is true moreover we obtain a simple fourier coefficient formula for f z ibukiyama 23 also made a similar conjecture which was formulated in terms of the koecher maass series which we will not consider here let us describe our results throughout this paper we fix positive integers k and n such that k n mod 2 and put e 1 k 1 n for any positive rational number n we denote the absolute value of the discriminant of q vn q by dn the primitive dirichlet character corresponding to q v n q is denoted by xn let fn be the positive rational number such that n nf2nlet b e m2n q be a positive definite half integral symmetric matrix put db det 2b db d db fb f db and xb x db note that edb 0 1 mod 4 and that fb is an integer for each prime p let p qp cx be the unique additive character such that bp x exp 27ir ltx for x e z p 1 recall that the siegel series for b is defined by

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

mechanisms of generation of the 2f2 f1 distortion product otoacoustic emission in humans the 2f1 f2 distortion product otoacoustic emission dpoae is considered to consist of two components in normally hearing ears one having constant phase with changing dp frequency wave fixed and one having an increasing phase lag with increasing frequency place fixed the aim was to identify the wave fixed and place fixed components of both 2f1 f2 and 2f2 f1 dps and in particular to show whether a wave fixed 2f2 f1 dp exists in normally hearing adults dpoae recordings were made in 20 ears of normally hearing young adults four frequency ratios were used and recording entailed fixed frequency ratio sweeps a separation into wave fixed and place fixed components was carried out using a time window separation method a method for estimating the noise floor after data processing was developed results confirmed the presence of wave fixed and place fixed components for 2f1 f2 consistent with previous studies both components were also present for 2f2 f1 in virtually all subjects this latter finding

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

congruence of siegel modular forms and special values of their standard zeta functions in this paper we consider the relationship between the congruence of cuspidal hecke eigenforms with respect to sp n z and the special values of their standard zeta functions in particular we propose a conjecture concerning the congruence between saito kurokawa lifts and non saito kurokawa lifts and prove it under certain condition

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

motives and siegel modular forms for a motive m over q we define the fundamental periods of m using invariant theory our definition generalizes deligne s periods we show that if a motive m is constructed from motives m 1 m 2 m n by a standard algebraic operation then the fundamental periods of m can be expressed as monomials of the fundamental periods of m 1 m 2 m n applying this theory we discuss two hypothetical motives attached to a siegel modular form we show that a siegel modular form of degree m has at most m 1 period invariants

uniqueness of multiplicative determinants on elliptic pseudodifferential operators we describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold that are continuous along continuous paths and the restriction to zero order operators of which is of class c1 this boils down to a description of all traces on zero order classical pseudodifferential operators which turn out to be linear combinations of the wodzicki residue w and leading symbol traces introduced in pr1 both of which are continuous consequently multiplicative determinants are parametrized by the residue determinant w87 sc and a new leading symbol determinant both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

on the coble quartic we obtain a short explicit expression for the universal coble quartic whose partial derivatives give the defining equations for the universal family of kummer threefolds the coble quartic was recently determined completely in ren sam schrader and sturmfels where theorem 7 1a it was computed explicitly as a polynomial with 372060 monomials of bidegree 28 4 in theta constants of the second order and theta functions of the second order respectively our expression is in terms of products of theta constants with characteristics corresponding to g opel systems and is a polynomial with 134 terms our approach is based on the beautiful geometry studied by coble and further investigated by dolgachev and ortland and highlights the geometry and combinatorics of syzygetic octets of characteristics the git quotient for 7 points in bf p 2 and the corresponding representations of rm sp 6 bbb f 2 one new ingredient is the relationship of g opel systems and jacobian determinants of theta functions in genus 2 we similarly obtain a short explicit equation for the universal kummer surface and relate modular forms of level two to binary invariants of six points on bf p 1

petersson norms of not necessarily cuspidal jacobi modular forms and applications abstract we extend the usual notion of petersson inner product on the space of cuspidal jacobi forms to include non cuspidal forms as well this is done by examining carefully the relation between certain growth killing invariant differential operators on h 2 and those on h 1 c here h n denotes the siegel upper half space of degree n as applications we can understand better the growth of petersson norms of fourier jacobi coefficients of klingen eisenstein series which in turn has applications to finer issues about representation numbers of quadratic forms and as a by product we also show that any siegel modular form of degree 2 is determined by its fundamental fourier coefficients

hochschild lefschetz class for mathcal d modules we introduce a notion of hochschild lefschetz class for a good coherent mathcal d module on a compact complex manifold and prove that this class is compatible with the direct image functor we prove an orbifold riemann roch formula for a mathcal d module on a compact complex orbifold

cortical responses to the 2f1 f2 combination tone measured indirectly using magnetoencephalography the simultaneous presentation of two tones with frequencies f1 and f2 causes the perception of several combination tones in addition to the original tones the most prominent of these are at frequencies f2 f1 and 2f1 f2 this study measured human physiological responses to the 2f1 f2 combination tone at 500hz caused by tones of 750 and 1000hz with intensities of 65 and 55db spl respectively responses were measured from the cochlea using the distortion product otoacoustic emission dpoae and from the auditory cortex using the 40 hz steady state magnetoencephalographic meg response the perceptual response was assessed by having the participant adjust a probe tone to cause maximal beating best beats with the perceived combination tone the cortical response to the combination tone was evaluated in two ways first by presenting a probe tone with a frequency of 460hz at the perceptual best beats level resulting in a 40 hz response because of interaction with the combination tone at 500hz and secon

homologie des invariants d une algebre de weyl sous l action d un groupe fini resume soit g un sous groupe fini de sp 2 n c operant par automorphismes dans l algebre de weyl a n c nous calculons les groupes d homologie et de cohomologie de hochschild de l algebre d invariants a n c g let g be a finite subgroup of sp 2 n c acting by automorphisms in the weyl algebra a n c we compute the hochschild homology and cohomology groups of the invariant algebra a n c g

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

examples of non kahler hamiltonian circle manifolds with the strong lefschetz property abstract in this paper we construct six dimensional compact non kahler hamiltonian circle manifolds which satisfy the strong lefschetz property themselves but nevertheless have a non lefschetz symplectic quotient this provides the first known counterexamples to the question whether the strong lefschetz property descends to the symplectic quotient we also give examples of hamiltonian strong lefschetz circle manifolds which have a non lefschetz fixed point submanifold in addition we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong lefschetz manifold we then use it to show the existence of lefschetz four manifolds with non lefschetz finite covering spaces

the effect of stimulus frequency ratio on distortion product otoacoustic emission components a detailed measurement of distortion product otoacoustic emission dpoae fine structure was used to extract estimates of the two major components believed to contribute to the overall dpoae level in the ear canal a fixed ratio paradigm was used to record dpoae fine structure from three normal hearing ears over a range of 400 hz for 12 different stimulus frequency ratios between 1 053 and 1 36 and stimulus levels between 45 and 75 db spl inverse fourier transforms of the amplitude and phase data were filtered to extract the early component from the generator region of maximum stimulus overlap and the later component reflected from the characteristic frequency region of the dpoae after filtering the data were returned to the frequency domain to evaluate the impact of the stimulus frequency ratio and stimulus level on the relative levels of the components although there were significant differences between data from different ears some consistent patterns could be detected the component from the overlap region of the stimulus tones exhibits a bandpass shape with the maximum occurring at a ratio of 1 2 the mean data from the dpoae characteristic frequency region also exhibits a bandpass shape but is less sharply tuned and exhibits greater variety across ears and stimulus levels the component from the dpoae characteristic frequency region is dominant at ratios narrower than approximately 1 1 the transition varies between ears the relative levels of the two components are highly variable at ratios greater than 1 3 and highly dependent on the stimulus level the reflection component is larger at all ratios at the lowest stimulus level tested 45 45 db spl we discuss the factors shaping dpoae component behavior and some cursory implications for the choice of stimulus parameters to be used in clinical protocols

distortion product otoacoustic emission delay measurement in human ears the measurement of distortion product otoacoustic emission dpoae delay using the phase gradient method is discussed a short f2 sweep paradigm is described its merits are discussed and comparisons made with other methods using sweeps of less than 4 consistent and reliable measurements were obtained from 12 normal ears except for a few isolated measurements investigation of these apparent anomalies indicated that the short f2 sweep method was sensitive to the localized effects of narrow distortion product intensity notches and spontaneous emissions it is possible that middle ear pressure instability or some local change in the cochlea sometimes compounded the situation the intersubject range 63 of the mean of dpoae delay values was greater than the range of values observed due to measurement variability 5 6 of the mean or intrasubject variability 8 5 of the mean demonstrating that the method can detect real differences between ears however comparison with previous work shows that caution is needed in interpreting these data as all dpoae phase methods provide only partial latency values the physical interpretation depends on both the stimulus sweep used and the origin of dpoaes our data shows that f1 sweep derived latency is lower than f2 sweep data by more than 20 caution also needs to be exercised when comparing cochlear traveling wave delay as inferred from electrophysiological data with that obtained from dpoae delay measurements

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

linear dependence among siegel modular forms theorems are given which describe when high enough vanishing at the cusps implies that a siegel modular cusp form is zero formerly impractical computations become practical and examples are given in degree four vanishing order is described by kernels a type of polyhedral convex hull

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

nonvanishing of koecher maass series attached to siegel cusp forms we prove a nonvanishing result for koecher maass series attached to siegel cusp forms of weight k and degree n in certain strips on the complex plane when n 2 we prove such a result for forms orthogonal to the space of the saito kurokawa lifts up to finitely many exceptions in bounded regions c 2015 elsevier inc all rights reserved

evidence for the distortion product frequency place as a source of distortion product otoacoustic emission dpoae fine structure in humans ii fine structure for different shapes of cochlear hearing loss distortion product otoacoustic emissions dpoae were recorded from eight human subjects with mild to moderate cochlear hearing loss using a frequency spacing of 48 primary pairs per octave and at a level l1 l2 60 dbspl and with a fixed ratio f2 f1 subjects with different shapes of hearing thresholds were selected they included subjects with near normal hearing within only a limited frequency range subjects with a notch in the audiogram and subjects with a mild to moderate high frequency loss if the primaries were located in a region of normal or near normal hearing but dp frequencies were located in a region of raised thresholds the distortion product 2 f1 f2 was still observable but the dp fine structure disappeared if the dp frequencies fell into a region of normal thresholds fine structure was preserved as long as dpoae were generated even in cases of mild hearing loss in the region of the primaries these experimental results give further strong evidence that in addition to the initial s

on a ring of modular forms related to the theta gradients map in genus 2 abstract the level moduli space of ppavs with a level structure a g 4 8 can be mapped to the projective space by means of the gradients of odd theta functions although this map is generically injective for g 3 it is not injective in the genus 2 case however there exists a congruence subgroup contained in 2 2 4 and containing 2 4 8 such that the theta gradient map factors on the quotient a of the siegel upper half plane by the group and the new map is injective on a we provide a description of this group together with some of its properties we also prove a structure theorem for the ring of modular forms a with respect to we finally provide a set of generators for the ideal of cusp forms s to give an algebraic description of the desingularization proj s of the satake compactification proj a

critical values of l functions on gsp 2 gl 2 this paper deals with deligne s conjecture on the critical values of l functions let z g h s denote the tensor product l function attached to a siegel modular form g of weight k and an elliptic cusp form h of weight l we assume that the first fourier jacobi coefficient of g is not identically zero then deligne s conjecture is fully proven for z g h s when l 2k 2 and partly for the remaining case

pullback of the lifting of elliptic cusp forms and miyawaki s conjecture we construct a lifting from siegel cusp forms of degree r to siegel cusp forms of degree r 2n for r n 1 our result is a partial solution of a conjecture made by miyawaki 27 page 307 in 1992 in particular we can calculate the standard l function of a cusp form of degree 3 and weight 12 which is in accordance with miyawaki s conjecture we give a conjecture on the petersson inner product of the lifting in terms of certain l values

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

characteristics of the 2f1 f2 distortion product otoacoustic emission in a normal hearing population distortion product otoacoustic emission dpoae fine structure and component characteristics are reported between 0 75 and 16 khz in 356 clinically normal hearing human subjects ages 10 to 65 yr stimulus tones at 55 40 65 55 and 75 75 db spl were delivered using custom designed drivers and a calibration method that compensated for the depth of insertion of the otoacoustic emission oae probe in the ear canal dpoae fine structure depth and spacing were found to be consistent with previous reports with depth varying between 3 and 7 db and average spacing ratios f f between 15 and 25 depending on stimulus level and frequency in general fine structure depth increased with increasing frequency likely due to a diminishing difference between dpoae component levels fine structure spacing became wider with increasing age above 8 khz dpoae components were extracted using the inverse fast fourier transform method adhering to a strict signal to noise ratio criterion for clearer interpretation component data from four age groups between 18 and 55 yr old were available for the stimulus levels of 75 75 db spl the age groups could be differentiated with greater than 90 accuracy when using the level of the component presumed to originate from the dpoae characteristic frequency place this accuracy held even for frequencies at and below 4 khz where the age groups exhibited similar average hearing thresholds

hard lefschetz theorem for sasakian manifolds we prove that on a compact sasakian manifold m g of dimension 2n 1 for any 0 p n the wedge product with d defines an isomorphism between the spaces of harmonic forms n p m and n p 1 m therefore it induces an isomorphism between the de rham cohomology spaces h m and h m such isomorphism is proven to be independent of the choice of a compatible sasakian metric on a given contact manifold as a consequence an obstruction for a contact manifold to admit sasakian structures is found

trace operators and theta series for γ 0 n q and γ n q we consider the action of suitable trace operators on non homogeneous theta series that are siegel modular forms for the principal congruence subgroups of the symplectic group of level q n q then we prove that modular forms for the hecke subgroup of level q 0 n q that are linear combination of such theta series can also be expressed as combination of homogeneous theta series that are modular forms with respect to 0 n q