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 are recent equidistribution results of N. Katz.

Revised according to referees' comments

Cited by in corpus (1)

• Correlations of multiplicative functions in function fields