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

2023/11/17 by Dousselin, Jérémy
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.10285

Abstract

Let F be a linear combination of N≥ 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× 10^-6/(Nlog N) is admissible for large N.

Related

• Zeros of Dirichlet L-functions on the critical line
• Critical zeros of Dirichlet L-functions
• Zeros of Dirichlet L-functions near the critical line
• The number of zeros of linear combinations of L-functions near the critical line
• Unconditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros