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October 2021 Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms
Huixue Lao, Shu Luo
Rocky Mountain J. Math. 51(5): 1701-1714 (October 2021). DOI: 10.1216/rmj.2021.51.1701

Abstract

We focus on the problems of sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms. Let λf(n), λg(n) and λh(n) be the n-th Fourier coefficients of primitive holomorphic cusp forms f, g and h for SL(2,), respectively. Firstly, we study the behavior of the signs of the sequences {λf(nj)} with j3, {λf(ni)λg(nj)} with i1,j2, and {λf(n)λg(n)λh(n)} in short intervals, and present some quantitative results for the number of sign changes for nx. Here we improve and generalize previous results. Moreover, we investigate simultaneous nonvanishing of {λf(nj)λg(nj)λh(nj)} with j1 in short intervals.

Citation

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Huixue Lao. Shu Luo. "Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms." Rocky Mountain J. Math. 51 (5) 1701 - 1714, October 2021. https://doi.org/10.1216/rmj.2021.51.1701

Information

Received: 9 October 2020; Accepted: 31 January 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1701

Subjects:
Primary: 11F11 , 11F30 , 11F66

Keywords: cusp form , Fourier coefficient , sign change , simultaneous nonvanishing

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 5 • October 2021
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