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.

引用

页数：20

共 50 条

[41] Quantum variance for Hecke eigenforms
Luo, WZ
Sarnak, P
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2004, 37 (05): : 769 - 799
[42] Shifted convolution sums of divisor functions with Fourier coefficients
Lou, Miao
JOURNAL OF NUMBER THEORY, 2024, 261 : 1 - 21
[43] Shifted convolution sums of fourier coefficients with divisor functions
Lu, G.
ACTA MATHEMATICA HUNGARICA, 2015, 146 (01) : 86 - 97
[44] SHIFTED CONVOLUTION SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS
Lau, Yuk-Kam
Liu, Jianya
Ye, Yangbo
NUMBER THEORY: SAILING ON THE SEA OF NUMBER THEORY, 2007, 2 : 108 - +
[45] Shifted convolution sums of fourier coefficients with divisor functions
G. Lü
Acta Mathematica Hungarica, 2015, 146 : 86 - 97
[46] Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues
Lu, Guangshi
Wang, Dan
JOURNAL OF NUMBER THEORY, 2019, 199 : 342 - 351
[47] Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues
Dan Wang
Indian Journal of Pure and Applied Mathematics, 2022, 53 : 443 - 453
[48] Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues
Wang, Dan
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (02): : 443 - 453
[49] Bounds of Multiplicative Character Sums over Shifted Primes
Bryce Kerr
Proceedings of the Steklov Institute of Mathematics, 2021, 314 : 64 - 89
[50] Polynomial identities between Hecke eigenforms
Bao, Dianbin
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2019, 15 (10) : 2135 - 2150

← 1 2 3 4 5 →