Correlations of Sums of Two Squares and Other Arithmetic Functions in Function Fields
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
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
Original language | English |
---|---|
Pages (from-to) | 4469-4515 |
Number of pages | 47 |
Journal | International Mathematics Research Notices |
Volume | 2019 |
Issue number | 14 |
Early online date | 9 Nov 2017 |
Publication status | Published - Jul 2019 |
Peer-reviewed | Yes |
External IDs
WOS | 000493552100010 |
---|---|
Scopus | 85077467996 |
Keywords
Keywords
- Asymptotic formula, Polynomial analog, Landaus theorem, Numbers, Intervals, Moments, Values