COMPARISON RESULTS FOR CERTAIN PERIODS OF CUSP FORMS ON GL2n OVER A TOTALLY REAL NUMBER FIELD
نویسنده
چکیده
This article grew out of my talk in ‘The Legacy of Srinivasa Ramanujan’ conference where I spoke about some techniques to prove algebraicity results for the special values of symmetric cube L-functions attached to the Ramanujan ∆-function. If one wishes to compare these different techniques, then one needs to compare various automorphic periods attached to the symmetric cube transfer of ∆. Motivated by this problem, in this article we provide comparison results for Whittaker-Betti periods, Shalika-Betti periods and relative periods attached to a given cohomological cuspidal automorphic representation of GL2n over a totally real number field.
منابع مشابه
Endoscopy and the cohomology of $GL(n)$
Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field. Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...
متن کاملNew Bounds for Automorphic L-functions
This dissertation contributes to the analytic theory of automorphic L-functions. We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation π of GLm over a number field. The approximation involves a smooth truncation of the Dirichlet series L(s, π) and L(s, π̃) after about √ C terms, where C denotes the analyti...
متن کاملHilbert Modular Forms with Prescribed Ramification
Let K be a totally real field. In this article we present an asymptotic formula for the number of Hilbert modular cusp forms f with given ramification at every place v of K. The meaning of “given ramification” needs to be made clear: when v is an infinite place, it means specifying the weight of f at k, and when v is finite, it means specifying the restriction to inertia of the local Weil-Delig...
متن کاملOn the Non-vanishing of the First Betti Number of Hyperbolic Three Manifolds
We show the non-vanishing of cohomology groups of sufficiently small congruence lattices in SL(1, D), where D is a quaternion division algebras defined over a number field E contained inside a solvable extension of a totally real number field. As a corollary, we obtain new examples of compact, arithmetic, hyperbolic three manifolds, with non-torsion first homology group, confirming a conjecture...
متن کاملArithmetic Aspects of the Theta Correspondence and Periods of Modular Forms
We review some recent results on the arithmetic of the theta correspondence for certain symplectic-orthogonal dual pairs and some applications to periods and congruences of modular forms. We also propose an integral version of a conjecture on Petersson inner products of modular forms on quaternion algebras over totally real fields.
متن کامل