torsion homology of arithmetic lattices and k_2 of imaginary fields let be a symmetric space of noncompact type a result of gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces we show that under suitable assumptions on this result can be extended to the case of nonuniform arithmetic lattices that may contain torsion using recent work of calegari and venkatesh we deduce from this upper bounds in terms of the discriminant for of the ring of integers of totally imaginary number fields more generally we obtain such bounds for rings of integers in f

the spherical fourier transform of rapidly decreasing functions a simple proof of a characterization due to harish chandra helgason trombi and varadarajan abstract harish chandra s helgason p c trombi and v s varadarajan have described the image of the l p schwartz spaces 0 p 2 under the spherical fourier transform we give a short proof of their results based on the paley wiener theorem

singular hyperbolic monopoles we study the twistor theory of singular hyperbolic su 2 monopoles following the approach taken by kronheimer 9 in the euclidean case we use our results to show that the moduli space of charge 1 monopoles possesses a natural 2 sphere of scalar flat kahler metrics in the zero mass limit the metrics reduce to a class of metrics first studied by lebrun in 10

ramanujanʼs master theorem for riemannian symmetric spaces abstract ramanujan s master theorem states that under suitable conditions the mellin transform of a power series provides an interpolation formula for the coefficients of this series based on the duality of compact and noncompact reductive riemannian symmetric spaces inside a common complexification we prove an analogue of ramanujan s master theorem for the spherical fourier transform of a spherical fourier series this extends the results proven by bertram for riemannian symmetric spaces of rank one

theorems of ingham and chernoff on riemannian symmetric spaces of noncompact type abstract an l 2 version of the celebrated denjoy carleman theorem regarding quasi analytic functions was proved by chernoff on r d using iterates of the laplacian in 1934 ingham used the classical denjoy carleman theorem to relate the decay of fourier transform and quasi analyticity of an integrable function on r in this paper we prove analogues of the theorems of chernoff and ingham for riemannian symmetric spaces of noncompact type and show that the theorem of ingham follows from that of chernoff

asymptotics of harish chandra expansions bounded hypergeometric functions associated with root systems and applications a series expansion for heckman opdam hypergeometric functions phi lambda is obtained for all lambda is an element of alpha c as a consequence estimates for phi lambda away from the walls of a weyl chamber are established we also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of helgason and johnson on the bounded spherical functions on a riemannian symmetric space of the noncompact type the l p theory for the hypergeometric fourier transform is developed for 0 p 2 in particular an inversion formula is proved when 1 p 2 c 2013 elsevier inc all rights reserved

the torsion in symmetric powers on congruence subgroups of bianchi groups in this paper we prove that for a fixed neat principal congruence subgroup of a bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m th symmetric power of the standard representation of sl 2 c grows exponentially in m 2 we give upper and lower bounds for the growth rate our result extends a a result of w muller and s marshall who proved the corresponding statement for closed arithmetic 3 manifolds to the finite volume case we also prove a limit multiplicity formula for combinatorial reidemeister torsions on higher dimensional hyperbolic manifolds

a unification of knizhnik zamolodchikov and dunkl operators via affine hecke algebras some generalizations of the lusztig lascoux schutzenberger operators for affine hecke algebras are considered as corollaries we obtain lusztig s isomorphisms from affine hecke algebras to their degenerate versions a natural interpretation of the dunkl operators and a new class of differential difference operators generalizing dunkl s ones and the knizhnik zamolodchikov operators from the two dimensional conformal field theory

positive convolution structure for a class of heckman opdam hypergeometric functions of type bc abstract in this paper we derive explicit product formulas and positive convolution structures for three continuous classes of heckman opdam hypergeometric functions of type bc for specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non compact grassmann manifolds g k over one of the skew fields f r c h we write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters in each of the three cases we obtain a series of hypergroup algebras which include the commutative convolution algebras of k biinvariant functions on g as special cases the characters are given by the associated hypergeometric functions

scattering theory for the laplacian on symmetric spaces of noncompact type and its application to a conjecture of strichartz abstract in this paper we develop the scattering theory for the laplacian on symmetric spaces of noncompact type we study the asymptotic properties of the resolvent in the framework of the agmon hormander space our approach is based on a detailed analysis of the helgason fourier transform and generalized spherical functions on symmetric spaces of noncompact type as an application of our scattering theory we prove a conjecture by strichartz concerning a characterization of a family of generalized eigenfunctions of the laplacian

geometry of hyper kahler connections with torsion the internal space of a n 4 supersymmetric model with wess zumino term has a connection with totally skew symmetric torsion and holonomy in sp n we study the mathematical background of this type of connection in particular we relate it to classical hermitian geometry construct homogeneous as well as inhomogeneous examples characterize it in terms of holomorphic data develop its potential theory and reduction theory

espace de schwartz pour la transformation de fourier hypergeometrique resume let r be a reduced root system in an euclidean vector space e w the weyl group of r one determines the hypergeometric fourier transform cf e opdam cuspidal hypergeometric functions preprint of the related schwartz space of w invariant functions on e introduced by tinfou the answer is very natural and quite similar to results of harish chandra the proof requires a theory of the constant term for w invariant functions satisfying the hypergeometric system this is analogous to harish chandra s theory once one has realized that simple difference operators play here the role of some elements of the unipotent radical of a parabolic subalgebra also the fact that the parameter of cuspidal hypergeometric functions might be singular introduces new difficulties this theory being established one can take advantage of the techniques we used for real reductive symmetric spaces cf the introduction to the article by the author formule de plancherel pour les espaces symetriques reductifs ann math 147 1998 417 452 especially the truncation and its consequences

an lp fourier analysis on symmetric spaces spherical fourier transforms of lp 1 p 2 functions on a riemannian symmetric space are studied it is proved that the spherical transform of such a function extends holomorphically to the same domain of the dual space as the one where the spherical transform of a schwartz function of lp type extends holomorphically and is rapidly decreasing cf 11 and also it is proved that a hausdorff young inequality and a riemann lebesgue lemma hold in the domain

a characterization of the l2 range of the poisson transform related to strichartz conjecture on symmetric spaces of noncompact type abstract the main purpose of this paper is to solve strichartz conjecture concerning an image characterization of the poisson transform in the l 2 theory on symmetric spaces of noncompact type we prove that the poisson transform provides an isomorphism between the l 2 space on the boundary and a certain weighted l 2 space consisting of joint eigenfunctions on symmetric spaces of noncompact type our approach is based on the scattering theory for the schrodinger operator moreover we give a fourier restriction estimate and an asymptotic formula for the poisson transform