THE BOUNDARY LERCH ZETA-FUNCTION AND SHORT CHARACTER SUMS À LA Y. YAMAMOTO

The Lerch zeta function IV. Hecke operators

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...

Hypergeometric Series Associated with the Hurwitz-lerch Zeta Function

The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.

Limit Theorem with Weight for Lerch Zeta Function

Weighted Short-interval Character Sums

In this paper we shall establish the counterpart of Szmidt, Urbanowicz and Zagier’s formula in the sense of the Hecker correspondence. The motivation is the derivation of the values of the Riemann zeta-function at positive even integral arguments from the partial fraction expansion for the hyperbolic cotangent function (or the cotangent function). Since the last is equivalent to the functional ...

Short Character Sums with Fermat Quotients

The distribution of Fermat quotients and related sequences is interesting from several perspectives. First, there are several applications, in particular to algebraic number theory and computer science. Fermat quotients play for instance a role in primality testing (see [L]) and are well-studied as model for generating pseudo-random numbers. (See [COW].) From the analytical side, establishing d...