scholarly journals Sums of Fourier coefficients of cusp forms of level $D$ twisted by exponential functions over arithmetic progressions

2017 ◽  
Vol 145 (9) ◽  
pp. 3761-3774
Author(s):  
Huan Liu ◽  
Meng Zhang
Keyword(s):  
Fourier Coefficients ◽  
Arithmetic Progressions ◽  
Cusp Forms ◽  
Exponential Functions

On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms

2014 ◽  
Vol 166 (3) ◽  
pp. 231-252
Author(s):  
Yujiao Jiang ◽  
Guangshi Lü
Keyword(s):  
Fourier Coefficients ◽  
Arithmetic Progressions ◽  
Cusp Forms

Fourier Coefficients of Modular Forms of Half-Integral Weight in Arithmetic Progressions

2020 ◽  
Author(s):  
Corentin Darreye
Keyword(s):  
Gaussian Distribution ◽  
Modular Forms ◽  
Prime Power ◽  
Fourier Coefficients ◽  
Arithmetic Progressions ◽  
Cusp Forms ◽  
Half Integral Weight ◽  
Mixed Distribution ◽  
Integral Weight ◽  
Holomorphic Cusp Forms

Abstract We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry–Ganguly–Kowalski–Michel and Kowalski–Ricotta in the context of half-integral weight holomorphic cusp forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution that comes from the asymptotic mixed distribution of Salié sums.

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

On averages of Fourier coefficients of Maass cusp forms

2013 ◽  
Vol 100 (3) ◽  
pp. 255-265 ◽  
Author(s):  
Guangshi Lü
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

On exponential sums for coefficients of general L-functions

2021 ◽  
pp. 1-22
Author(s):  
Fei Hou
Keyword(s):  
Functional Equation ◽  
General Formula ◽  
Fourier Coefficients ◽  
Exponential Sums ◽  
Exponential Functions ◽  
Maass Forms ◽  
Maass Form ◽  
Rapid Decay

We investigate the order of exponential sums involving the coefficients of general [Formula: see text]-functions satisfying a suitable functional equation and give some new estimates, including refining certain results in preceding works [X. Ren and Y. Ye, Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for [Formula: see text], Sci. China Math. 58(10) (2015) 2105–2124; Y. Jiang and G. Lü, Oscillations of Fourier coefficients of Hecke–Maass forms and nonlinear exponential functions at primes, Funct. Approx. Comment. Math. 57 (2017) 185–204].

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