Prime polynomial values of linear functions in short intervals

Efrat Bank; Lior Bary-Soroker

doi:https://doi.org/10.1016/j.jnt.2014.12.016

Prime polynomial values of linear functions in short intervals

Efrat Bank, Lior Bary-Soroker

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	263-275
Number of pages	13
Journal	Journal of Number Theory
Volume	151
DOIs	https://doi.org/10.1016/j.jnt.2014.12.016
State	Published - 1 Jun 2015

Keywords

Function fields
Polynomials
Prime Number Theorem
Primes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1016/j.jnt.2014.12.016

Cite this

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N2 - 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.

AB - 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.

KW - Function fields

KW - Polynomials

KW - Prime Number Theorem

KW - Primes

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M3 - مقالة

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VL - 151

SP - 263

EP - 275

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Prime polynomial values of linear functions in short intervals

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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