References & Citations
Mathematics > Number Theory
Title: Twisted correlations of the divisor function via discrete averages of $\operatorname{SL}_2(\mathbb{R})$ Poincaré series
(Submitted on 12 Apr 2024 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms to study Poincar\'e series over congruence subgroups. By keeping track of interactions between multiple orbits we get advantages over the widely used sums of Kloosterman sums techniques. We showcase this with applications to correlations of the divisor functions twisted by periodic functions and the fourth moment of Dirichlet $L$-functions on the critical line.
Submission history
From: Jori Merikoski [view email][v1] Fri, 12 Apr 2024 14:31:35 GMT (59kb)
[v2] Fri, 26 Apr 2024 15:04:28 GMT (55kb)
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