Equidistribution of Fourier coefficients of integral weight Maass-Poincare series

被引：0

作者：

Masri, Riad ^{[1
]}

Tsai, Wei-Lun ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Math, Mailstop 3368, College Stn, TX 77843 USA

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

ADVANCES IN MATHEMATICS | 2022年 / 409卷

关键词：

Equidistribution; Fourier coefficient; Weak Maass form; Sato-Tate measure; PRODUCTS;

D O I：

10.1016/j.aim.2022.108637

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the normalized Fourier coefficients of a generic family of Maass-Poincare series of integral weight k and prime level p become quantitatively equidistributed with respect to the Sato-Tate measure as p -> infinity. As a consequence, we deduce similar results for harmonic Maass forms of integral weight k <= 0 and level p, and weakly holomorphic modular forms of integral weight k >= 2 and level p.(C) 2022 Elsevier Inc. All rights reserved.

引用

页数：28

共 50 条

[41] On Fourier coefficients of modular forms of half integral weight at squarefree integers
Jiang, Y. -J.
Lau, Y. -K.
Lue, G. -S.
Royer, E.
Wu, J.
MATHEMATISCHE ZEITSCHRIFT, 2019, 293 (1-2) : 789 - 808
[42] FOURIER COEFFICIENTS OF MODULAR-FORMS OF HALF-INTEGRAL WEIGHT
IWANIEC, H
INVENTIONES MATHEMATICAE, 1987, 87 (02) : 385 - 401
[43] ON A PROPERTY OF FOURIER COEFFICIENTS OF CUSP FORMS OF HALF-INTEGRAL WEIGHT
MIYAKE, T
MAEDA, Y
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1994, 34 (02): : 463 - 473
[44] THE SIGN OF FOURIER COEFFICIENTS OF HALF-INTEGRAL WEIGHT CUSP FORMS
Hulse, Thomas A.
Kiral, E. Mehmet
Kuan, Chan Ieong
Lim, Li-Mei
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (03) : 749 - 762
[45] A note on the Fourier coefficients of half-integral weight modular forms
Narasimha Kumar
Soma Purkait
Archiv der Mathematik, 2014, 102 : 369 - 378
[46] A note on the Fourier coefficients of half-integral weight modular forms
Kumar, Narasimha
Purkait, Soma
ARCHIV DER MATHEMATIK, 2014, 102 (04) : 369 - 378
[47] On some estimates involving Fourier coefficients of Maass cusp forms
Sun, Qingfeng
Wang, Hui
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, 19 (05) : 997 - 1019
[48] Quadratic forms connected with Fourier coefficients of Maass cusp forms
Hu, Liqun
FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (05) : 1101 - 1112
[49] ADDITIVE TWISTS OF FOURIER COEFFICIENTS OF GL(3) MAASS FORMS
Li, Xiannan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (06) : 1825 - 1836
[50] Quadratic forms connected with Fourier coefficients of Maass cusp forms
Liqun Hu
Frontiers of Mathematics in China, 2015, 10 : 1101 - 1112

← 1 2 3 4 5 →