Fourier coefficients of cusp forms on special sequences

被引:0
作者
Yao, Weili [1 ,2 ]
机构
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China
基金
中国国家自然科学基金;
关键词
Fourier coefficient; cusp forms; symmetric power L-functions; short intervals; POWER SUMS; EIGENVALUES;
D O I
10.1142/S1793042124500568
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we investigate the square of the normalized Fourier coefficients of the primitive cusp forms f and its symmetric-lift at integers with a fixed number of distinct prime divisors, and present asymptotic formulas for them in short intervals.
引用
收藏
页码:1161 / 1190
页数:30
相关论文
共 50 条
[31]   The average value of Fourier coefficients of cusp forms in arithmetic progressions [J].
Lue, Guangshi .
JOURNAL OF NUMBER THEORY, 2009, 129 (02) :488-494
[32]   SIGN CHANGES AND NONVANISHING OF FOURIER COEFFICIENTS OF HOLOMORPHIC CUSP FORMS [J].
Lao, Huixue ;
Luo, Shu .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2022, 51 (05) :1701-1714
[33]   Fourier coefficients of cusp forms and automorphic F-functions [J].
Fomenko O.M. .
Journal of Mathematical Sciences, 1999, 95 (3) :2295-2316
[34]   An analogue of the Bombieri–Vinogradov Theorem for Fourier coefficients of cusp forms [J].
Ratnadeep Acharya .
Mathematische Zeitschrift, 2018, 288 :23-37
[35]   General asymptotic formula of Fourier coefficients of cusp forms over sum of two squares [J].
Xu, Chenran .
JOURNAL OF NUMBER THEORY, 2022, 236 :214-229
[36]   On exponential sums involving Fourier coefficients of cusp forms over primes [J].
Hou, Fei .
JOURNAL OF NUMBER THEORY, 2016, 164 :375-404
[37]   A Generalization of kohnen’s estimates for fourier coefficients of siegel cusp forms [J].
T. Horie .
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1997, 67 :47-63
[38]   A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS [J].
Das, Soumya ;
Ganguly, Satadal .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (06) :2301-2305
[39]   High power sums of Fourier coefficients of holomorphic cusp forms and their applications [J].
Hu, Guangwei ;
Lao, Huixue ;
Pan, Huimin .
AIMS MATHEMATICS, 2024, 9 (09) :25166-25183
[40]   Sums of k-th powers and Fourier coefficients of cusp forms [J].
Zhining Wei .
The Ramanujan Journal, 2023, 60 :295-316