Zeros of linear twists of $L$-functions outside the critical strip

Abstract

In this note we investigate the existence of zeros of linear twists of $L$-functions outside of the critical strip. In particular, we show that the Lerch zeta function $L(\lambda ,\alpha ,s)$ has infinitely many zeros for $1<\sigma <1+\eta$, for any $\eta >0$, when $\lambda$ is irrational and $\alpha$ is rational. This settles the question on the existence of zeros of the Lerch zeta functions for $\sigma >1$.

Cited by in corpus (1)

• A note on the universality of Hurwitz-Lerch zeta functions