Number fields and function fields: coalescences, contrasts and emerging applications

Author:

Keating J. P.1,Rudnick Z.2,Wooley T. D.1

Affiliation:

1. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK

2. Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israels

Abstract

The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field. Although an active area of interaction for the past half century at least, the language and techniques used in analytic number theory and in the function field setting are quite different, and this has frustrated interchanges between the two areas. This situation is currently changing, and there has been substantial progress on a number of problems stimulated by bringing together ideas from each field. We here introduce the papers published in this Theo Murphy meeting issue, where some of the recent developments are explained.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Roots of Polynomials and the Derangement Problem;The American Mathematical Monthly;2018-11-26

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