title: Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t].
abstract: In this paper, we solve a function field analogue of classical problems in analytic number theory, concerning the autocorrelations of divisor functions, in the limit of a large finite field.
authors: Institut des Hautes Études Scientifiques (IHÉS), Le Bois-Marie, 35 Route de Chartres, Bures-sur-Yvette 91440, France j.c.andrade.math@gmail.com.
authors: J C
authors: JC
authors: Andrade
authors: Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
authors: L
authors: L
authors: Bary-Soroker
authors: Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
authors: Z
authors: Z
authors: Rudnick
keywords: cycle structure; divisor function; finite fields; function fields; random permutation; shifted convolution