Hardy-littlewood tuple conjecture over large finite fields

Lior Bary-Soroker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the following function field analog of the Hardy-Littlewood conjecture (which generalizes the twin prime conjecture) over large finite fields. Let n and r be positive integers and q an odd prime power. For a tuple of distinct polynomials of degree <n let π(q,n;a) be the number of monic polynomials of degree n such that f+a1,f+ar are simultaneously irreducible. We prove that as and n,r fixed.

Original languageEnglish
Pages (from-to)568-675
Number of pages108
JournalInternational Mathematics Research Notices
Volume2014
Issue number2
DOIs
StatePublished - Oct 2014

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