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

Zeev Rudnick

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

School of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The lecture 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 Möbius function; and the additive divisor problem.

Original language	English
Title of host publication	Invited Lectures
Editors	Sun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
Publisher	KYUNG MOON SA Co. Ltd.
Pages	443-459
Number of pages	17
ISBN (Electronic)	9788961058056
State	Published - 2014
Event	2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of Duration: 13 Aug 2014 → 21 Aug 2014

Publication series

Name	Proceeding of the International Congress of Mathematicans, ICM 2014
Volume	2

Conference

Conference	2014 International Congress of Mathematicans, ICM 2014
Country/Territory	Korea, Republic of
City	Seoul
Period	13/08/14 → 21/08/14

Keywords

Chowla's conjecture
Function fields over a finite field
Primes in short intervals
The additive divisor problem

Cite this

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Some problems in analytic number theory for polynomials over a finite field. / Rudnick, Zeev.

Invited Lectures. ed. / Sun Young Jang; Young Rock Kim; Dae-Woong Lee; Ikkwon Yie. KYUNG MOON SA Co. Ltd., 2014. p. 443-459 (Proceeding of the International Congress of Mathematicans, ICM 2014; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

Abstract

Publication series

Conference

Keywords

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Cite this