Fourier coefficients of Eisenstein series formed with modular symbols and their spectral decomposition

Bruggeman, Roelof; Diamantis, Nikolaos

Abstract

The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum.

Citation

Bruggeman, R., & Diamantis, N. (2016). Fourier coefficients of Eisenstein series formed with modular symbols and their spectral decomposition. Journal of Number Theory, 167, https://doi.org/10.1016/j.jnt.2016.03.009

• Journal Article Type: Article
• Acceptance Date: Mar 8, 2016
• Online Publication Date: Apr 16, 2016
• Publication Date: Oct 1, 2016
• Deposit Date: Jun 30, 2016
• Publicly Available Date: Jun 30, 2016
• Journal: Journal of Number Theory
• Print ISSN: 0022-314X
• Electronic ISSN: 1096-1658
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 167
• DOI: https://doi.org/10.1016/j.jnt.2016.03.009
• Keywords: Shifted convolution sums; Spectral decomposition; Second order Maass forms
• Public URL: https://nottingham-repository.worktribe.com/output/974601
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0022314X16300567
• Contract Date: Jun 30, 2016