A note on the universality of Hurwitz-Lerch zeta functions

TL;DR

This paper discusses the challenges in establishing the universality of the Lerch zeta function under specific irrationality and algebraic conditions, highlighting the difficulties faced in such proofs.

Contribution

It provides insights into the limitations and obstacles encountered in proving the universality of Lerch zeta functions for certain irrational and algebraic parameter cases.

Findings

Failed to prove universality in specified cases

Identifies key difficulties in extending universality results

Highlights the need for new approaches in zeta function theory

Abstract

A failed attempt to prove the universality of Lerch zeta function $L(\lambda,\alpha,s)$ when $\lambda$ is irrational and $\alpha$ is rational, and for any $\lambda$ when $\alpha$ is irrational algebraic.