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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)4469-4515
Seitenumfang47
FachzeitschriftInternational Mathematics Research Notices
Jahrgang2019
Ausgabenummer14
Frühes Online-Datum9 Nov. 2017
PublikationsstatusVeröffentlicht - Juli 2019
Peer-Review-StatusJa

Externe IDs

WOS 000493552100010
Scopus 85077467996

Schlagworte

Schlagwörter

  • Asymptotic formula, Polynomial analog, Landaus theorem, Numbers, Intervals, Moments, Values