Self-approximation of 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.

Dirichlet L-functions, Elliptic Curves, Hypergeometric Functions, and Rational Approximation with Partial Sums of Power Series

We consider the Diophantine approximation of exponential generating functions at rational arguments by their partial sums and by convergents of their (simple) continued fractions. We establish quantitative results showing that these two sets of approximations coincide very seldom. Moreover, we offer many conjectures about the frequency of their coalescence. In particular, we consider exponentia...

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...