On exponential sums involving Fourier coefficients of cusp forms

JOURNAL OF NUMBER THEORY

卷:132

Article

Liu, Kui¹  Ren, Xiumin¹ 

[1] Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China

关键词: Modular form for SL(2)(Z);    Fourier coefficients;    Exponential sum;    Voronoi summation formula;   

DOI  :  10.1016/j.jnt.2011.07.003

来源: Elsevier

【 摘 要 】

Let a(n) be the normalized Fourier coefficient of a holomorphic cusp form of weight k or a Maass cusp form with Laplacian eigenvalue 1/4 + r(2) for SL(2)(Z). We consider exponential sum of the form Sigma(n <= x)a(n)e(alpha n(2) + beta n) and obtain the upper bound X(7/8+epsilon) which is uniformly in alpha, beta is an element of R. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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