height pairings on shimura curves and p adic uniformization in a recent paper 16 of one of us it was shown that there is a close connection between the value of the height pairing of certain arithmetic 0 cycles on shimura curves and the values at the center of their symmetry of the derivatives of certain metaplectic eisenstein series of genus 2 on the one hand the height pairing can be written as a sum of local height pairings for example if the 0 cycles have disjoint support on the generic fiber then their height pairing is a sum of an archimedean contribution and a contribution from each of the finitely many finite primes p for which the cycles meet in the fiber at p on the other hand it turns out that the non singular part of the fourier expansion of the central derivative of the metaplectic eisenstein series also has a decomposition into a sum of contributions indexed by the places of q then one would like to compare the height pairing and the fourier coefficients by proving an identity of local contributions place by place in loc cit the identity for the archimedean place was proved and it was shown that the identity at a non archimedean place of good reduction is a consequence of results of gross and keating 10 for the algebraicgeometric side and of kitaoka 12 for the analytic side it then remains to consider the finite primes p where the shimura curve has bad reduction these are of three sorts i the primes p at which the quaternion algebra defining the shimura curve is split but which divide the level ii the primes p at which the quaternion algebra remains division but no level structure is imposed and iii the primes p at which the quaternion algebra remains division and where a higher level structure is imposed at p so far little is known concerning cases i and iii

counting points on igusa varieties igusa varieties are smooth varieties over fp which are higher dimensional analogues of igusa curves they were introduced by harris and taylor ht to study the bad reduction of some pel shimura varieties and were generalized by mantovan m1 m2 the present article gives a group theoretic formula for the traces of certain operators on the cohomology of igusa varieties suitable for applications via comparison with the arthur selberg trace formula our formula generalizes the results of ht chap v prop 4 8 to the case of any pel shimura varieties of types a and c and puts it in a more natural framework in the spirit of k7

the mass of extremal doubly even self dual codes of length 40 we determine the mass of extremal doubly even self dual binary codes of length 40 it follows that there are at least 12579 such codes

maass relations in higher genus for an arbitrary even genus 2n we show that the subspace of siegel cusp forms of degree 2n generated by ikeda lifts of elliptic cusp forms can be characterized by certain linear relations among fourier coefficients this generalizes the classical maass relations in degree two to higher degrees

stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

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

on certain zeta functions attached to two hilbert modular forms ii the case of automorphic forms on a quaternion algebra as to the meaning of the symbols the reader is referred to the introduction of part i we recall here only that f is a totally real algebraic number field of degree n and w denotes the fourier coefficients of an elliptic modular form 52 z e wq a e2q iaz in part i we investigated d assuming that ex a n q s is an l function of a cm field with an algebraic valued hecke character in the present part ii we treat the case where x a can be obtained as eigenvalues of hecke operators t a on a quaternion algebra b over f thus we begin our study by recalling the theory of automorphic forms on the product o r of r copies of the upper half plane with respect to congruence subgroups of b x here r is the number of archimedean primes of f unramified in b then we introduce in section 2 the notion of arithmeticity or q rationality of such automorphic forms and show that the space of automorphic forms can be spanned by the arithmetic ones our main theorems will be stated in section 3 and proved in section 6 sections 4 and 5 are preliminaries to the proof the central result specialized to the case r 1 asserts that if g is a q rational eigenform such that gj t a x a g for all integral ideals a of f then d s0 for certain integers so are algebraic numbers times 7tdg g where d is an integer determined by the weight of g and is the petersson inner product

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

nonlinear observers for perspective time invariant linear systems perspective dynamical systems arise in machine vision in which only perspective observation is available this paper proposes and studies a luenberger type nonlinear observer for perspective time invariant linear systems assuming a given perspective time invariant linear system to be lyapunov stable and to satisfy some sort of detectability condition it is shown that the estimation error converges exponentially to zero finally some simple numerical examples are presented to illustrate the result obtained

the l2 lefschetz numbers of hecke operators introduction 5 1 hecke operators and l2 cohomology 52 the spectral decomposition of cohomology 6 3 application of the trace formula 54 the functions pa t 5 5 proof of theorem 5 1 6 the main formula appendix bibliography

special cycles on unitary shimura varieties i unramified local theory the supersingular locus in the fiber at p of a shimura variety attached to a unitary similitude group gu 1 n 1 over is uniformized by a formal scheme mathcal n in the case when p is an inert prime we define special cycles mathcal z bold x in mathcal n associated to collections bold x of m special homomorphisms with fundamental matrix t hermm ok when m n and t is nonsingular we show that the cycle mathcal z bold x is either empty or is a union of components of the ekedahl oort stratification and we give a necessary and sufficient condition in terms of t for mathcal z bold x to be irreducible when mathcal z bold x is zero dimensional in which case it reduces to a single point we determine the length of the corresponding local ring by using a variant of the theory of quasi canonical liftings we show that this length coincides with the derivative of a representation density for hermitian forms

brief paper observer design for range and orientation identification a reduced order globally convergent observer to estimate the depth of an object projected on the image plane of a camera is presented assuming that the object is planar or has a planar surface and the orientation of the plane is known a locally convergent observer can be obtained when the plane unit normal is unknown and the latter is estimated together with the depth of the object the observer exploits the image moments of the object as measured features the estimation is achieved by rendering attractive and invariant a manifold in the extended state space of the system and the observer the problem is reduced to the solution of a system of partial differential equations the solution of the partial differential equations can become a difficult task hence it is shown that this issue can be resolved by adding to the observer an output filter and a dynamic scaling parameter

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

motion estimation via dynamic vision estimating the three dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics such as autonomous navigation manipulation servo tracking docking planning and surveillance although visual motion estimation is an old problem the first formulations date back to the beginning of the century only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions in this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold such a formulation has structural advantages over previous recursive schemes since the estimation of motion is decoupled from the estimation of the structure of the object being viewed and therefore it is possible to handle occlusions in a principled way

arithmetic properties of fourier jacobi expansions of automorphic forms in several variables in this paper we establish some basic arithmetic results concerning automorphic forms in several variables our results are in part analogues of the classical facts for elliptic modular forms and results of shimura on hilbert and siegel modular forms 9 and 10 in essence this involves relating rationality properties of fourier jacobi coefficients to rationality properties in algebraic geometry our automorphic forms are c valued holomorphic functions on certain cartesian powers hnd of siegel upper half spaces hn we consider appropriate arithmetic groups r acting on hnd such that r h d is noncompact in particular we reduce our study to that of congruence subgroups r of reductive linear algebraic groups g such that the derived group g is almost simple over q further let k be a maximal compact subgroup of g r the connected component of the identity in the real

cell decomposition of some unitary group rapoport zink spaces in this paper we study the p adic analytic geometry of the basic unitary group rapoport zink spaces mathcal m k with signature 1 n 1 using the theory of harder narasimhan filtration of finite flat groups developed in fargues journal fur die reine und angewandte mathematik 645 1 39 2010 fargues theorie de la reduction pour les groupes p divisibles prepublications http www math jussieu fr fargues prepublications html 2010 and the bruhat tits stratification of the reduced special fiber mathcal m red defined in vollaard and wedhorn invent math 184 591 627 2011 we find some relatively compact fundamental domain mathcal d k in mathcal m k for the action of g mathbb q p times j b mathbb q p the product of the associated p adic reductive groups and prove that mathcal m k admits a locally finite cell decomposition by considering the action of regular elliptic elements on these cells we establish a lefschetz trace formula for these spaces by applying mieda s main theorem in mieda lefschetz trace formula for open adic spaces preprint arxiv 1011 1720 2013

on the cohomology of rapoport zink spaces of el type in this article we are interested in determining the l adic cohomology of rapoport zink spaces associated to rm gl n over an unramified extension of bbb q p called unramified el type in connection with the local langlands correspondence for rm gl n in fact we compute the alternating sum of certain representation theoretic functors defined in terms of their cohomology on the level of grothendieck groups in case rapoport zink spaces parametrize p divisible groups of dimension one the above alternating sum is determined by harris and taylor without the unramifiedness assumption for p divisible groups of rm dim 1 fargues has obtained an answer for the supercuspidal part when the p divisible groups are basic i e their associated newton polygons are straight lines our main result is an identity among the cohomology of rapoport zink spaces that appear in the newton stratification of the same unitary shimura variety our result implies a theorem of fargues providing a second proof and reveals new information about the cohomology of rapoport zink spaces for non basic p divisible groups we propose an inductive procedure to completely determine the above alternating sum assuming a strengthening of our main result along with a conjecture of harris

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

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

an explicit formula for siegel series combining induction formulas for local densities with a functional equation for the siegel series we give an explicit formula for the siegel series by this formula we also give an explicit formula for the fourier coefficients of the siegel eisenstein series

correction to poles and residues of standard l functions attached to siegel modular forms correction to my paper on the poles of standard l functions attached to siegel modular forms

explicit formulas for the twisted koecher maas series of the duke imamoglu ikeda lift and their applications we give an explicit formula for the twisted koecher maas series of the duke imamoglu ikeda lift as an application we prove a certain algebraicity result for the values of twisted rankin selberg series at integers of half integral weight modular forms which was not treated by shimura j math soc japan 33 649 672 1981

values of symmetric cube l functions and fourier coefficients of siegel eisenstein series of degree 3 we obtain formulas for certain weighted sums of values of the symmetric square and triple product l functions as a consequence we get exact values at the right critical point for the symmetric square and symmetric cube l functions attached to certain cuspforms we also give applications to fourier coefficients of modular forms

fourier coefficients of siegel eisenstein series of odd genus abstract we give a new expression of the t th fourier coefficients of the siegel eisenstein series of odd genus unlike even genus case only modified divisor sums and no generalized class numbers enter into our formula

3 d structure from visual motion modeling representation and observability abstract the problem of structure from motion concerns the reconstruction of the three dimensional structure of a scene from its projection onto a moving two dimensional surface such a problem is solved effectively by the human visual system judging from the ease with which we perform delicate control tasks involving vision as a sensor such as reaching for objects in the environment or driving a car in this paper we study structure from motion from the point of view of dynamical systems we first formalize the problem of 3 d structure and motion reconstruction as the estimation of the state of certain nonlinear dynamical models then we study the feasibility of structure from motion by analyzing the observability of such models the models that define the visual motion estimation problem for feature points in the euclidean 3 d space are not locally observable however the non observable manifold can be easily isolated by imposing metric constraints on the state space one of the peculiarities of vision as a sensor is its richness which can be a disadvantage when we are interested only in few of the unknown parameters for instance if we want to control the direction of heading of our car by measuring brightness values on our retina we have to overcome the effects that the shape of the environment its reflectance properties illumination and other quantities have on our measurements invariance to undesired parameters can be achieved by appropriate modeling or by choice of representation of the parameter space we propose and analyze models for 3 d structure that are independent of 3 d motion and vice versa estimating unknown parameters from such models amounts to the identification of nonlinear and implicit systems with parameters on differentiable manifolds such as a sphere or the so called essential manifold 1997 elsevier science ltd

on the cohomology of certain pel type shimura varieties in this article we study the local geometry at a prime p of pel type shimura varieties for which there is a hyperspecial level subgroup we consider the newton polygon stratification of the special fiber at p of shimura varieties and show that each newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding pel type rapoport zink spaces with certain smooth varieties which we call igusa varieties and of the action on them of a p adic group that depends on the stratum we then extend our construction to characteristic zero and in the case of bad reduction at p use it to compare the vanishing cycle sheaves of the shimura varieties to those of the rapoport zink spaces as a result of this analysis in the case of proper shimura varieties we obtain a description of the l adic cohomology of the shimura varieties in terms of the l adic cohomology with compact supports of the igusa varieties and of the rapoport zink spaces for any prime l p

on the local density formula and the gross keating invariant with an appendix the local density of a binary quadratic form by t ikeda and h katsurada ikeda and katsurada have developed the theory of the gross keating invariant of a quadratic form in their recent papers ikeda and katsurada am j math 140 1521 1565 2018 explicit formula of the siegel series of a quadratic form over a non archimedean local field 2017 arxiv 1602 06617 in particular they prove that the local factors of the fourier coefficients of the siegel eisenstein series are completely determined by the gross keating invariants with extra datums called the extended gk datums in ikeda and katsurada explicit formula of the siegel series of a quadratic form over a non archimedean local field 2017 arxiv 1602 06617 on the other hand such a local factor is a special case of the local density for a pair of two quadratic forms thus we propose a general question if the local density can be expressed in terms of a certain series of extended gk datums in this paper we prove that the answer to this question is affirmative for the local density of a single quadratic form defined over an unramified finite extension of mathbb z 2 and over a finite extension of mathbb z p with p odd in the appendix ikeda and katsurada compute the local density formula of a single binary quadratic form defined over any finite extension of mathbb z 2

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

zeta functions and eisenstein series on classical groups we construct an euler product from the hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a cm field and the eigenform is holomorphic we also prove analytic continuation of an eisenstein series on another unitary group containing the group just mentioned defined with such an eigenform as an application of our methods we prove an explicit class number formula for a totally definite hermitian form over a cm field

some remarks on triple l functions we extend the garrett s result i 4 concerning triple l function in two aspects one concerns triple l functions of different weights and the other concerns special values of triple l functions of same weights at inner points of their critical strips let mk fn and sk fn be spaces of siegel modular forms and cuspforms of weight k and of degree n respectively for siegel modular forms f l fro of various degree and a field k we denote by k ft fro the field generated by all the fourier coefficients of f l fro over k we write fourier expansion of f sk f1

the weil representation and hecke operators for vector valued modular forms we define hecke operators for vector valued modular forms transforming with the weil representation associated to a discriminant form we describe the properties of the corresponding algebra of hecke operators and study the action on modular forms

inertial sensor bias estimation from brightness depth images and based on so 3 invariant integro partial differential equations on the unit sphere constant biases associated to measured linear and angular velocities of a moving object can be estimated from measurements of a static scene by embedded brightness and depth sensors we propose here a lyapunov based observer taking advantage of the so 3 invariance of the partial differential equations satisfied by the measured brightness and depth fields the resulting asymptotic observer is governed by a nonlinear integro partial differential system where the two independent scalar variables indexing the pixels live on mathbb s 2 the observer design and analysis are strongly simplified by coordinate free differential calculus on mathbb s 2 equipped with its natural riemannian structure the observer convergence is investigated under c 1 regularity assumptions on the object motion and its scene it relies on the ascoli arzela theorem and precompactness of the observer trajectories it is proved that the estimated biases converge towards the true ones if and only if the scene admits no cyl

visual modeling with a hand held camera in this paper a complete system to build visual models from camera images is presented the system can deal with uncalibrated image sequences acquired with a hand held camera based on tracked or matched features the relations between multiple views are computed from this both the structure of the scene and the motion of the camera are retrieved the ambiguity on the reconstruction is restricted from projective to metric through self calibration a flexible multi view stereo matching scheme is used to obtain a dense estimation of the surface geometry from the computed data different types of visual models are constructed besides the traditional geometry and image based approaches a combined approach with view dependent geometry and texture is presented as an application fusion of real and virtual scenes is also shown

three dimensional motion computation and object segmentation in a long sequence of stereo frames we address the problem of computing the three dimensional motions of objects in a long sequence of stereo frames our approach is bottom up and consists of two levels the first level deals with the tracking of 3d tokens from frame to frame and the estimation of their kinematics the processing is completely parallel for each token the second level groups tokens into objects based on their kinematic parameters controls the processing at the low level to cope with problems such as occlusion disappearance and appearance of tokens and provides information to other components of the system we have implemented this approach using 3d line segments obtained from stereo as the tokens we use classical kinematics and derive closed form solutions for some special but useful cases of motions the motion computation problem is then formulated as a tracking problem in order to apply the extended kalman filter the tracking is performed in a prediction matching update loop in which multiple matches can be handled tokens are labeled by a number called its support of existence which measures their adequation to the measurements if this number goes beyond a threshold the token disappears the individual line segments can be grouped into rigid objects according to the similarity of their kinematic parameters experiments using synthetic and real data have been carried out and the results found to be quite good

on the bloch kato conjecture for elliptic modular forms of square free level let kappa ge 6 be an even integer m an odd square free integer and f in s 2 kappa 2 gamma 0 m a newform we prove that under some reasonable assumptions that half of the lambda part of the bloch kato conjecture for the near central critical value l kappa f is true we do this by bounding the ell valuation of the order of the appropriate bloch kato selmer group below by the ell valuation of algebraic part of l kappa f we prove this by constructing a congruence between the saito kurokawa lift of f and a cuspidal siegel modular form

ikeda s conjecture on the period of the duke imamoḡlu ikeda lift let k and n be positive even integers for a cus pidal hecke eigenform h in the kohnen plus subspace of weight k n 2 1 2 for 0 4 let in h be the duke imamoglu ikeda lift of h in the space of cusp forms of weight k for spn z and f the primitive form of weight 2k n for sl2 z corresponding to h under the shimura correspondence we then express the ratio hin h in h i hh hi of the period of in h to that of h in terms of special values of certain l functions of f this proves the conjecture proposed by ikeda concerning the period of the duke imamoglu ikeda lift one of the fascinating problems in the theory of modular forms is to find the relation between the periods or the petersson products of cuspidal hecke eigenforms which are related with each other through their l functions in particular there are several important results concerning the relation between the period of a cuspidal hecke eigen form g for an elliptic modular group sl2 z and that of its lift bhere by a lift of g we mean a cuspidal hecke eigenform for another modular group 0 e g the symplectic group the orthogonal group the unitary group etc whose certain l function can be expressed in terms of certain l functions related with g thus we propose the following problem problem a express the ratio hbbi hg gi e in terms of arithmetic invariants of g for example the special values of certain l functions related with g for some integer e for instance zagier zag77 solved problem a for the doi naganuma

on certain zeta functions attached to two hilbert modular forms i the case of hecke characters to make our exposition smooth let us first introduce some notational conventions for an algebraic number field k of finite degree we denote by jk the set of all embeddings of k into c and by ik the free z module generated by the elements of jk we then put rik ik0 r and cik ik0 c if p eapau e ik with a e jk and po e z we put xp fl xa pfor 0 x e k this is meaningful for p e cik if xa are all real and positive throughout the paper we denote by d the complex upper half plane and by f a totally real algebraic number field of degree n now the zeta function to be studied in this paper when suitably specialized has the form

confluent hypergeometric functions on tube domains our problem specialized to the case of the siegel upper half space h of degree m concerns the fourier expansion of a series s z fl det z a det a a l here z is a variable on h l is a lattice in the space v of all real symmetric matrices of size m and fl ec it can be shown that this is convergent if re f l m and also that if re m 2 and r e f l m 2 it has a fourier expansion of the form

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

sign changes in harmonic analysis on reductive groups let g be a connected reductive group over a field f in this note the author constructs an element e g of the brauer group of f the square of this element is trivial for a local field e g may be regarded as an element of i and is needed for harmonic analysis on reductive groups over that field for a global field there is a product formula the purpose of this note is to provide a cohomological interpretation of the sign changes in harmonic analysis on reductive groups over local fields that are caused by inner twistings the best understood example occurs in the work of shelstad 8 on inner twistings of real groups theorem 6 3 of that paper gives the following character identity 1 q g q g x here g is a connected reductive group over r g is its quasi split inner form x and x are stabilized characters of matched tempered l packets of g r and g r and y and y are matched regular semisimple elements of g r and g r the sign change in the character identity is q g q g where q g is one half of the dimension of the symmetric space attached to g more precisely attached to the simply connected cover of the derived group of g although q g may be only half integral the difference q g q g is always integral it is reasonable to expect an analogous character identity for groups g over a nonarchimedean local field f we can determine what the sign change must be by considering the steinberg characters of g f and g f since these should be related by the character identity let r g denote the f rank of the derived group of g the steinberg character of g f has value i r g on the elliptic regular set of g f and hence the sign change in the character identity must be l r g r g there are two groups for which the character identity has been proved the multiplicative group of a central division algebra of dimension d2 over f for d 2 see proposition 15 5 on p 484 of 4 and d 3 see theorem 1 of 1 later in this paper we will use a cohomological construction to define a sign e g 1 for any connected reductive group g over a local field let g denote a quasi split inner form of g we will show that e g l r g r g when the base received by the editors may 10 1982 1980 mathematics subject classification primary 22e50 partially supported by the national science foundation under grant mcs 78 02331 1983 american mathematical society 0002 9947 82 0000 11 93 03 25

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

classicality for small slope overconvergent automorphic forms on some compact pel shimura varieties of type c we study the rigid cohomology of the ordinary locus in some compact pel shimura varieties of type c with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent hecke eigenforms this generalises work of coleman and is a first step in an ongoing project to extend the cohomological approach to classicality to higher dimensional shimura varieties

an explicit arithmetic formula for the fourier coefficients of siegel eisenstein series of degree two and square free odd levels we give an explicit arithmetic formula for the fourier coefficients of siegel eisenstein series of degree two and square free odd levels

a mass formula for unimodular lattices with no roots we derive a mass formula for n dimensional unimodular lattices having any prescribed root system we use katsurada s formula for the fourier coefficients of siegel eisenstein series to compute these masses for all root systems of even unimodular 32 dimensional lattices and odd unimodular lattices of dimension n 30 in particular we find the mass of even unimodular 32 dimensional lattices with no roots and the mass of odd unimodular lattices with no roots in dimension n 30 verifying bacher and venkov s enumerations in dimensions 27 and 28 we also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the minkowski siegel mass constants