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December 2017 Oscillations of Fourier coefficients of $GL(m)$ Hecke-Maass forms and nonlinear exponential functions at primes
Yujiao Jiang, Guangshi Lü
Funct. Approx. Comment. Math. 57(2): 185-204 (December 2017). DOI: 10.7169/facm/1623

Abstract

Let $F(z)$ be a Hecke-Maass form for $SL(m,\mathbb{Z})$ and $A_F(n,1, \dots, 1)$ be the coefficients of $L$-function attached to $F.$ We study the cancellation of $A_F(n,1, \dots, 1)$ for twisted with a nonlinear exponential function at primes, namely the sum \begin{equation*} \sum_{n \leq N} \Lambda (n)A_F(n,1, \dots, 1)e ( \alpha n^\theta ), \end{equation*} where $0<\theta<2/m$. We also strengthen the corresponding previous results for holomorphic cusp forms for $SL(2,\mathbb{Z}),$ and improve the estimates of Ren-Ye on the resonance of exponential sums involving Fourier coefficients of a Maass form for $SL(m,\mathbb{Z})$.

Citation

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Yujiao Jiang. Guangshi Lü. "Oscillations of Fourier coefficients of $GL(m)$ Hecke-Maass forms and nonlinear exponential functions at primes." Funct. Approx. Comment. Math. 57 (2) 185 - 204, December 2017. https://doi.org/10.7169/facm/1623

Information

Published: December 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864171
MathSciNet: MR3732895
Digital Object Identifier: 10.7169/facm/1623

Subjects:
Primary: 11F30
Secondary: 11F66, 11L07, 11L20

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 2 • December 2017
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