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

Jon P Keating; Z Rudnick

doi:10.1093/imrn/rns220

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

Jon P Keating, Z Rudnick

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Article number	rns220
Number of pages	30
Journal	International Mathematics Research Notices
Volume	October 16, 2012
DOIs	https://doi.org/10.1093/imrn/rns220
Publication status	Published - 16 Oct 2012

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title = "The variance of the number of prime polynomials in short intervals and in residue classes",

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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DO - 10.1093/imrn/rns220

M3 - Article (Academic Journal)

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VL - October 16, 2012

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

M1 - rns220

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

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