Hybrid joint universality theorem for Dirichlet L-functions

Calculation of Dirichlet L-Functions

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.

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

On the Order of Dirichlet L-functions

Real zeros of quadratic Dirichlet L - functions

A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...

The Mean-square of Dirichlet L-functions

where α and β are small complex numbers satisfying α, β ≪ 1/ log q. Ingham [Ing] considered an analogous moment for the Riemann zeta-function on the critical line with small shifts. Paley [Pal] considered the moment above for Dirichlet L-functions. Heath-Brown [HB] has computed a similar moment, but for all characters modulo q, in the case that α = β = 0. His result is Theorem 1 (HB). There are...