Zeros of L(s)+L(2s)+⋯+L(Ns) in the region of absolute convergence

2019/09/18 by Pańkowski, Łukasz, Righetti, Mattia
#11M26 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.08301

Abstract

In this paper we show that for every Dirichlet L-function L(s,χ) and every N≥ 2 the Dirichlet series L(s,χ)+L(2s,χ)+⋯+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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