The Lerch zeta function IV. Hecke operators

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...

The Ihara-Selberg zeta function for PGL3 and Hecke operators

A weak version of the Ihara formula is proved for zeta functions attached to quotients of the Bruhat-Tits building of PGL3. This formula expresses the zeta function in terms of Hecke-Operators. It is the first step towards an arithmetical interpretation of the combinatorially defined zeta function.

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

The Partition Function and Hecke Operators

The theory of congruences for the partition function p(n) depends heavily on the properties of half-integral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P (z) | T (`), where P (z) is the relevant modular generating function. We obtain such formulas using Euler’s Pentagonal Number Theorem and the denominator formula for the Mons...