The Semi Simple Zeta Function Of Quaternionic Shimura Varieties
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The semi-simple zeta function of quaternionic Shimura varieties
This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.
Advances in the Theory of Automorphic Forms and Their $L$-functions
Author: Dihua Jiang
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-04-29
This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their L-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna. The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their L-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of p-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, L-functions for classical groups, special values of L-functions, Howe duality, subconvexity for L-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on L-functions, nodal sets and geometry.
Harmonic Analysis, the Trace Formula, and Shimura Varieties
Author: Clay Mathematics Institute. Summer School
language: en
Publisher: American Mathematical Soc.
Release Date: 2005
Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.