Correlations of Sums of Two Squares and Other Arithmetic Functions in Function Fields

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Abstract

We investigate a function field analogue of a recent conjecture on autocorrelations of sums of two squares by Freiberg, Kurlberg, and Rosenzweig, which generalizes an older conjecture by Connors and Keating. In particular, we provide extensive numerical evidence and prove it in the large finite field limit. Our method can also handle correlations of other arithmetic functions and we give applications to (function field analogues of) the average of sums of two squares on shifted primes, and to autocorrelations of higher divisor functions twisted by a quadratic character.

Original languageEnglish
Pages (from-to)4469-4515
Number of pages47
JournalInternational Mathematics Research Notices
Volume2019
Issue number14
DOIs
StatePublished - 1 Jul 2019

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