Work

A modular framework for functions of Knopp and indefinite binary quadratic forms

Year: 2025

Type: article

Abstract: We study functions introduced by Knopp and complete them to non-holomorphic bimodular forms of positive integral weight related to indefinite binary quadratic forms. We investigate further properties of our completions, which in turn motivates certain local cusp forms. We then define modular analogues of negative weight of our local cusp forms, which are locally harmonic Maass forms with continuously removable singularities. We show that they admit local splittings in terms of Eichler integrals.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500920

Authors: Kathrin Bringmann, Andreas Mono

Institutions: University of Cologne, Vanderbilt University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Deutsche Forschungsgemeinschaft

Awards: G242263537, TRR 191: Symplektische Strukturen in Geometrie, Algebra und Dynamik, G8615234819