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arXiv · 1609.01058

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

Mattia Righetti
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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 $\sigma>1$.

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Mattia Righetti. 2016-09-05. Zeros of linear twists of $L$-functions outside the critical strip. https://arxiv.org/abs/1609.01058

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