Arithmetic Correlations Over Large Finite Fields

Jonathan P. Keating, Edva Roditty-Gershon*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
289 Downloads (Pure)

Abstract

The auto-correlations of arithmetic functions, such as the von Mangoldt function, the Mo bius function, and the divisor function, are the subject of classical problems in analytic number theory The function field analogs of these problems have recently been resolved in the limit of large finite field size q. However, in this limit, the correlations disappear: the arithmetic functions become uncorrelated. We compute averages of terms of lower order in q which detect correlations. Our results show that there is considerable cancellation in the averaging and have implications for the rate at which correlations disappear when q → ∞ in particular, one cannot expect remainder terms that are of the order of the square-root of the main term in this context.

Original languageEnglish
Pages (from-to)860-874
Number of pages15
JournalInternational Mathematics Research Notices
Volume2016
Issue number3
Early online date4 Jun 2015
DOIs
Publication statusPublished - Mar 2016

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