Nonvanishing of Dirichlet L-functions
نویسندگان
چکیده
منابع مشابه
Nonvanishing of quadratic Dirichlet L - functions at s
The Generalized Riemann Hypothesis (GRH) states that all non-trivial zeros of Dirichlet L-functions lie on the line Re(s) = 12 . Further, it is believed that there are no Q-linear relations among the non-negative ordinates of these zeros. In particular, it is expected that L( 1 2 , χ) 6= 0 for all primitive characters χ, but this remains still unproved. This appears to have been first conjectur...
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In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...
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Motivated by work of Gross, Rohrlich, and more recently Kim, Masri, and Yang, we investigate the nonvanishing of central values of L-functions of “canonical” weight 2k−1 Hecke characters for Q( √ −p), where 3 < p ≡ 3 (mod 4) is prime. Using the work of Rodriguez-Villegas and Zagier, we show that there are nonvanishing central values provided that p ≥ 6.5(k−1) and (−1) ( 2 p ) = 1. Moreover, we ...
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In [Ja-Sh], Jacquet and Shalika use the spectral theory of Eisenstein series to establish a new result concerning the nonvanishing of L-functions on <(s) = 1. Specifically they show that the standard L-function L(s, π) of an automorphic cusp form π on GLm is nonzero for <(s) = 1. We analyze this method, make it effective and also compare it with the more standard methods. This note is based on ...
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A method for calculating Dirichlet L-series is presented along with the theory of residue class characters and their automatic generation. Tables are given of zeros of Lseries for moduli S 24.
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2016
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2016.10.2081