Growth of the Lerch zeta-function

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

ON THE q-EXTENSIONS OF THE BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND LERCH ZETA FUNCTION

Recently, λ-Bernoulli and λ-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the q-extensions of the λBernoulli and the λ-Euler numbers by using the bosonic p-adic q-integral and the fermionic p-adic q-integral. The investigation of these λ-q-Bernoulli and λ-q-Euler numbers leads to interesting identities related to these objec...

Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function

Keywords: Hurwitz–Lerch Zeta function Lipschitz–Lerch Zeta function Lerch Zeta function Hurwitz Zeta function Riemann Zeta function Legendre chi function Bernoulli polynomials Bernoulli numbers Discrete Fourier transform a b s t r a c t It is shown that there exists a companion formula to Srivastava's formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bern...