Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke–Maass L-functions in the critical strip

The Second Moment of Dirichlet Twists of Hecke L-functions

Artin L - Functions in the Critical Strip

This paper gives a method for computing values of certain nonabelian Artin ¿-functions in the complex plane. These Artin ¿-functions are attached to irreducible characters of degree 2 of Galois groups of certain normal extensions K of Q. These fields K are the ones for which G = Gal(.KyQ) has an abelian subgroup A of index 2, whose fixed field Q(\/d) is complex, and such that there is a a S G —...

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...

Nonvanishing of L-functions of Cusp Forms inside the Critical Strip

A theorem of W. Kohnen states that the generalized Riemann hypothesis (GRH) holds on an average for holomorphic cusp forms on the upper half plane for the full modular group SL2(Z). In this article we prove a couple of generalizations of this theorem of Kohnen that the GRH holds on an average for holomorphic cusp forms on the upper half plane for arbitrary level, weight and primitive nebentypus...

Nonvanishing of certain Rankin-Selberg L-functions

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...