Work

Laurent expansions of meromorphic modular forms

Year: 2024

Type: article

Abstract: In this paper, we study the Laurent coefficients of meromorphic modular forms at complex multiplication points by giving two approaches of computing them. The first is a generalization of the method of Rodriguez‐Villegas and Zagier, which expresses the Laurent coefficients as constant terms of a family of polynomials obtained through recursion. The second applies to meromorphic modular forms that are regularized theta lifts, and expresses their Laurent coefficients in terms of Fourier coefficients of harmonic Maass forms.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70036

Authors: Gabriele Bogo, Yingkun Li, Markus Schwagenscheidt

Institutions: Bielefeld University, ETH Zurich

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Deutsche Forschungsgemeinschaft, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung