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Nonvanishing of twists of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}L$-functions attached to Hilbert modular forms

Part of: Discontinuous groups and automorphic forms Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  01 August 2014

Nathan C. Ryan ,
Gonzalo Tornaría  and
John Voight
Nathan C. Ryan
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA email nathan.c.ryan@gmail.com
Gonzalo Tornaría
Affiliation:
Centro de Matemática, Universidad de la República, 11400 Montevideo, Uruguay email tornaria@cmat.edu.uy
John Voight
Affiliation:
Department of Mathematics , Dartmouth College , 6188 Kemeny Hall , Hanover, NH 03755 , USA email jvoight@gmail.com

Abstract

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We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and predictions from random matrix theory.

MSC classification

Secondary: 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11M50: Relations with random matrices 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 330 - 348
Copyright
© The Author(s) 2014 

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