Prime polynomial values of linear functions in short intervals

Efrat Bank; Lior Bary-Soroker

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arXiv · 1410.1283

Prime polynomial values of linear functions in short intervals

Efrat Bank·Lior Bary-Soroker

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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 values of $n$ linear functions, in the limit of a large finite field.

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Efrat Bank, Lior Bary-Soroker. 2014-10-06. Prime polynomial values of linear functions in short intervals. https://arxiv.org/abs/1410.1283

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