Conditional lower bounds on the distribution of central values in families of L-functions

2023/07/31 by Maksym Radziwiłł, K. Soundararajan, Radziwiłł, Maksym +1 · 3 citations
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.00169

openalex publication_date 2023/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a general principle that any lower bound on the non-vanishing of central L-values obtained through studying the one-level density of low-lying zeros can be refined to show that most such L-values have the typical size conjectured by Keating and Snaith. We illustrate this technique in the case of quadratic twists of a given elliptic curve, and similar results would hold for the many examples studied by Iwaniec, Luo, and Sarnak in their pioneering work on 1-level densities.

Cited by

• Linear Combinations of Logarithms of L-functions over Function Fields at Microscopic Shifts and Beyond
• Selberg orthogonality for half-integral weight modular forms
• Regulators of the fixed elliptic curve over rank-one imaginary quadratic fields

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