Prime polynomial values of linear functions in short intervals

Efrat Bank, Lior Bary-Soroker

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we establish a function field analogue of a conjecture in number theory which is a combination of several famous conjectures, including the Hardy-Littlewood prime tuple conjecture, conjectures on the number of primes in arithmetic progressions and in short intervals, and the Goldbach conjecture. We prove an asymptotic formula for the number of simultaneous prime polynomial values of n linear functions, in the limit of a large finite field.

Original languageEnglish
Pages (from-to)263-275
Number of pages13
JournalJournal of Number Theory
Volume151
DOIs
StatePublished - 1 Jun 2015

Keywords

  • Function fields
  • Polynomials
  • Prime Number Theorem
  • Primes

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