Zeros of linear combinations of Dirichlet $L$-functions on the critical line

Jérémy Dousselin

Zeros of linear combinations of Dirichlet $L$-functions on the critical line

Number Theory 2023-12-01 v2

Authors: Jérémy Dousselin

Abstract

Let $F$ be a linear combination of $N\geq 1$ Dirichlet $L$ -functions attached to even (or odd) primitive characters with the same modulus. Selberg proved that a positive proportion of non-trivial zeros of $F$ lie on the critical line. Our work here is to provide an explicit lower bound for this proportion. In particular, we show that the lower bound $2.16\times 10^{-6}/(N\log N)$ is admissible for large $N$ .

Keywords

dirichlet l-functions linear combination critical line non-trivial zeros explicit lower bound primitive characters

Cite

@article{arxiv.2311.10285,
  title  = {Zeros of linear combinations of Dirichlet $L$-functions on the critical line},
  author = {Jérémy Dousselin},
  journal= {arXiv preprint arXiv:2311.10285},
  year   = {2023}
}

Comments

Corrected typos and rephrased statements of the two main theorems

Zeros of linear combinations of Dirichlet $L$-functions on the critical line

Abstract

Keywords

Cite

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