The Variance of the Number of Prime Polynomials in Short Intervals and in Residue Classes

Keating, Jonathan P.; Rudnick, Zeév

doi:10.1093/imrn/rns220

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The Variance of the Number of Prime Polynomials in Short Intervals and in Residue Classes

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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 is the recent equidistribution results of N. Katz.

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The Variance of the Number of Prime Polynomials in Short Intervals and in Residue Classes

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