Some problems in analytic number theory for polynomials over a finite field

2015/01/08 by Zeév Rudnick, Zeev Rudnick, Rudnick, Zeev · 1 citation
Computer Science · Mathematics · #11T55 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11T55

paper · pdf · doi:10.48550/arxiv.1501.01769

Minor fixes and updated references over the published version of the ICM 2014 proceedings

arxiv created 2015/01/08 · openalex publication_date 2015/01/08 · arxiv updated 2015/01/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The lecture, given at the ICM 2014 in Seoul, explores several problems of analytic number theory in the context of function fields over a finite field, where they can be approached by methods different than those of traditional analytic number theory. The resulting theorems can be used to check existing conjectures over the integers, and to generate new ones. Among the problems discussed are: Counting primes in short intervals and in arithmetic progressions; Chowla's conjecture on the autocorrelation of the Mobius function; and the additive divisor problem.

Cited by

• Central limit theorems for random multiplicative functions over function fields

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• Finite field models in additive combinatorics
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