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arXiv · 2308.00169

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

Maksym Radziwiłł·Kannan Soundararajan
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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.

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Maksym Radziwiłł, Kannan Soundararajan. 2023-07-31. Conditional lower bounds on the distribution of central values in families of $L$-functions. https://arxiv.org/abs/2308.00169

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