Joint universality for Lerch zeta-functions

TL;DR

This paper proves joint universality properties of Lerch zeta-functions with different parameters, extending the understanding of their value distribution in the complex plane.

Contribution

It establishes the joint universality for Lerch zeta-functions with distinct parameters and transcendental alpha, a novel result in the field.

Findings

Proved joint universality for Lerch zeta-functions with distinct lambda parameters.

Extended universality results to functions with transcendental alpha.

Enhanced understanding of the value distribution of Lerch zeta-functions.

Abstract

For $0<\alpha, \lambda \leq 1$, the Lerch zeta-function is defined by $L(s;\alpha, \lambda)$$:= \sum_{n=0}^\infty e^{2\pi i\lambda n} (n+\alpha)^{-s}$, where $\sigma>1$. In this paper, we prove joint universality for Lerch zeta-functions with distinct $\lambda_1,\ldots,\lambda_m$ and transcendental $\alpha$.