The variance of the number of prime polynomials in short intervals and in residue classes

J. P. Keating; Z. Rudnick

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arXiv · 1204.0708

The variance of the number of prime polynomials in short intervals and in residue classes

J. P. Keating·Z. Rudnick

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Abstract

We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent equidistribution results of N. Katz.

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J. P. Keating, Z. Rudnick. 2012-04-03. The variance of the number of prime polynomials in short intervals and in residue classes. https://arxiv.org/abs/1204.0708

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