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arXiv · 1909.08301

Zeros of $L(s)+L(2s)+\cdots+L(Ns)$ in the region of absolute convergence

Łukasz Pańkowski·Mattia Righetti
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Abstract

In this paper we show that for every Dirichlet $L$-function $L(s,χ)$ and every $N\geq 2$ the Dirichlet series $L(s,χ)+L(2s,χ)+\cdots+L(Ns,χ)$ have infinitely many zeros for $σ>1$. Moreover we show that for many general $L$-functions with an Euler product the same holds if $N$ is sufficiently large, or if $N=2$. On the other hand we show with an example the the method doesn't work in general for $N=3$.

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BibTeXRIS

Łukasz Pańkowski, Mattia Righetti. 2019-09-18. Zeros of $L(s)+L(2s)+\cdots+L(Ns)$ in the region of absolute convergence. https://arxiv.org/abs/1909.08301

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