Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Integral power sums of Fourier coefficients of symmetric square $ L$-functions


Author: Xiaoguang He
Journal: Proc. Amer. Math. Soc. 147 (2019), 2847-2856
MSC (2010): Primary 11F30, 11F11, 11F66
DOI: https://doi.org/10.1090/proc/14516
Published electronically: March 26, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f(z)$ be a holomorphic Hecke eigenform of even weight $ k$ for $ \operatorname {SL}(2,\mathbb{Z})$, and denote $ L(s, \mathrm {sym}^2f)$ be the corresponding symmetric square $ L$-function associated to $ f$. Suppose that $ \lambda _{\mathrm {sym}^2f} (n)$ is the $ n$th normalized Fourier coefficient of $ L(s, \mathrm {sym}^2f)$. In this paper, we investigate the sum $ \sum _{n\leq x}\lambda ^j_{\mathrm {sym}^2f}(n)$ for $ j=2,3,4$, and get some new results which improve the previous results.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F30, 11F11, 11F66

Retrieve articles in all journals with MSC (2010): 11F30, 11F11, 11F66


Additional Information

Xiaoguang He
Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People’s Republic of China
Email: hexiaoguangsdu@gmail.com

DOI: https://doi.org/10.1090/proc/14516
Keywords: Cusp forms, Fourier coefficients, symmetric square $L$-function
Received by editor(s): June 18, 2018
Received by editor(s) in revised form: October 30, 2018
Published electronically: March 26, 2019
Additional Notes: The author is grateful to the China Scholarship Council (CSC) for supporting his studies at The Pennsylvania State University.
Communicated by: Amanda Folsom
Article copyright: © Copyright 2019 American Mathematical Society