A note on the universality of Hurwitz-Lerch zeta functions

Mattia Righetti

Published 2016-12-02Version 1

In this note we show that the Lerch zeta function $L(\lambda,\alpha,s)$ is strongly universal when $\lambda$ is irrational and $\alpha$ is rational, and for any $\lambda$ when $\alpha$ is irrational algebraic. This settles in the positive the conjecture that Lerch zeta functions, and in particular Hurwitz zeta functions, are universal for any choice of its parameters and strongly universal except for the obvious cases.