On the fourth power moment of Fourier coefficients of cusp form

Authors
Li, Jin Jiang Wang, Pan Wang Zhang, Min
Citation
Li, Jin Jiang et al., On the fourth power moment of Fourier coefficients of cusp form, Acta mathematica Sinica. English series (Print) , 34(6), 2018, pp. 1050-1058
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
6
Year of publication
2018
Pages
1050 - 1058
Database
ACNP
SICI code
Abstract
Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight . = 2n . 12 for the full modular group and A(x) = .n.xa(n). In this paper, we establish an asymptotic formula of the fourth power moment of A(x) and prove that .T1A4(x)dx=364..4s4;2(a~)T2.+O(T2...4+.) with .4 = 1/8, which improves the previous result.