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Session S09 - Number Theory in the Americas

Thursday, July 15, 12:30 ~ 13:00 UTC-3

Sums of certain arithmetic functions over $\mathbb{F}_q[T$] and symplectic distributions

Matilde Lalin

U. Montreal, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak4cbf7ffa97207c782be7bc299b346674').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy4cbf7ffa97207c782be7bc299b346674 = 'ml&#97;l&#105;n' + '&#64;'; addy4cbf7ffa97207c782be7bc299b346674 = addy4cbf7ffa97207c782be7bc299b346674 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text4cbf7ffa97207c782be7bc299b346674 = 'ml&#97;l&#105;n' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak4cbf7ffa97207c782be7bc299b346674').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy4cbf7ffa97207c782be7bc299b346674 + '\'>'+addy_text4cbf7ffa97207c782be7bc299b346674+'<\/a>';

In 2018 Keating, Rodgers, Roditty-Gershon and Rudnick established relationships of the mean-square of sums of the divisor function $d_k(f)$ over short intervals and over arithmetic progressions for the function field $\mathbb{F}_q[T]$ to certain integrals over the ensemble of unitary matrices. We consider similar problems leading to distributions over the ensemble of symplectic matrices. We also consider analogous questions involving convolutions of the von Mangoldt function.

Joint work with Vivian Kuperberg (Stanford U., USA).