Zeros of L-Functions in Low-Lying Intervals and de Branges spaces

2024/04/11 by Antonio Pedro Ramos, Ramos, Antonio Pedro
Mathematics · #11F66 #11M26 #11M41 #42A05 #46E22 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.07832

openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a variant of a problem first introduced by Hughes and Rudnick (2003) and generalized by Bernard (2015) concerning conditional bounds for small first zeros in a family of L-functions. Here we seek to estimate the size of the smallest intervals centered at a low-lying height for which we can guarantee the existence of a zero in a family of L-functions. This leads us to consider an extremal problem in analysis which we address by applying the framework of de Branges spaces, introduced in this context by Carneiro, Chirre, and Milinovich (2022).

Related

• Small first zeros of L-functions
• Hilbert spaces and low-lying zeros of L-functions
• Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros
• Unconditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros
• Conditional lower bounds on the distribution of central values in families of L-functions