Modular iterated integrals associated with cusp forms

Diamantis, Nikolaos

Abstract

We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing modular invariant functions based on iterated integrals of modular forms. The construction will be based on an extension of higher-order modular forms which, in contrast to the standard higher-order forms, applies to general Fuchsian groups of the first kind and, as such, is of independent interest.

Citation

Diamantis, N. (2022). Modular iterated integrals associated with cusp forms. Forum Mathematicum, 34(1), 157-174. https://doi.org/10.1515/forum-2021-0224

• Journal Article Type: Article
• Acceptance Date: Oct 1, 2021
• Online Publication Date: Dec 1, 2021
• Publication Date: Jan 1, 2022
• Deposit Date: Mar 1, 2022
• Publicly Available Date: Dec 2, 2022
• Journal: Forum Mathematicum
• Print ISSN: 0933-7741
• Electronic ISSN: 1435-5337
• Publisher: Walter de Gruyter GmbH
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 1
• Pages: 157-174
• DOI: https://doi.org/10.1515/forum-2021-0224
• Keywords: Applied Mathematics; General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/6842859
• Publisher URL: https://www.degruyter.com/document/doi/10.1515/forum-2021-0224/html