Bounds on shifted convolution sums for Hecke eigenforms

被引：4
|
作者：
Nordentoft, Asbjorn C. [1 ]
Petridis, Yiannis N. [2 ]
Risager, Morten S. [3 ]
机构：
[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany
[2] UCL, Dept Math, Gower St, London WC1E 6BT, England
[3] Univ Copenhagen, Dept Math Sci, Univ Pk, DK-2100 Copenhagen O, Denmark
来源：
RESEARCH IN NUMBER THEORY | 2022年 / 8卷 / 02期
关键词：
Shifted convolution sums; SELBERG L-FUNCTIONS; FOURIER COEFFICIENTS; CUSP FORMS; SQUARE; SIEVE;
D O I：
10.1007/s40993-022-00320-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Shifted convolution sums play a prominent role in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.
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页数：20
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