The distribution of values of zeta and L-functions

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arxiv 2112.03389 v1 pith:SEPRXKL7 submitted 2021-12-06 math.NT

Kannan Soundararajan This is my paper · ORCID

classification math.NT

keywords distributionl-functionszetaarticleintendedprogressrecentsurvey

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This is a survey of recent progress on understanding the value distribution of zeta and L-functions. The article is intended for the 2022 ICM.

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An Explicit Tauberian Theorem taking Averaged Inputs with an Application to Counting Abelian Number Fields
math.NT 2025-08 conditional novelty 7.0 of 10

An explicit Tauberian theorem using twisted moment bounds instead of pointwise bounds yields square-root-saving error terms for counting C_n-extensions of Q for n = 3, 4, 8, 16, and 2p.