Kernels of L-functions and shifted convolutions

Diamantis, Nikolaos

Abstract

We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's technique to study multiple modular values with the properties of a double Eisentein series previously studied by the author and C. O'Sullivan.

Citation

Diamantis, N. (2020). Kernels of L-functions and shifted convolutions. Proceedings of the American Mathematical Society, 148, 5059-5070. https://doi.org/10.1090/proc/15182

• Journal Article Type: Article
• Acceptance Date: May 11, 2020
• Online Publication Date: Sep 17, 2020
• Publication Date: Sep 17, 2020
• Deposit Date: Jul 4, 2020
• Publicly Available Date: Sep 17, 2020
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 148
• Pages: 5059-5070
• DOI: https://doi.org/10.1090/proc/15182
• Keywords: Number Theory
• Public URL: https://nottingham-repository.worktribe.com/output/2463712
• Additional Information: First published in Proceedings of the American Mathematical Society in 2020, published by the American Mathematical Society.