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Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms

Dorigoni, Daniele; Kleinschmidt, Axel; Schlotterer, Oliver

Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms Thumbnail


Authors

Axel Kleinschmidt

Oliver Schlotterer



Abstract

We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two non-holomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of single-valued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their L-values inside and outside the critical strip.

Citation

Dorigoni, D., Kleinschmidt, A., & Schlotterer, O. (2022). Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms. Journal of High Energy Physics, 2022(1), Article 134. https://doi.org/10.1007/jhep01%282022%29134

Journal Article Type Article
Acceptance Date Dec 25, 2021
Online Publication Date Jan 25, 2022
Publication Date 2022-01
Deposit Date Oct 12, 2021
Publicly Available Date May 11, 2022
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2022
Issue 1
Article Number 134
DOI https://doi.org/10.1007/jhep01%282022%29134

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http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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