Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms
Journal article, 2021

The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals. Applications beyond number theory range from combinatorics, geometry, and representation theory to string theory and conformal field theory. We unify these relaxed notions in the framework of vector-valued modular forms by introducing a new class of SL (ℤ)-representations: virtually real-arithmetic types. The key point of the paper is that virtually real-arithmetic types are in general not completely reducible. We obtain a rationality result for Fourier and Taylor coefficients of associated modular forms.

Author

Michael H. Mertens

University of Liverpool

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

Published in

Mathematical Research Letters

1073-2780 (ISSN) 1945001x (eISSN)

Vol. 28 Issue 2 p. 511-561

Categorizing

Subject Categories (SSIF 2011)

Algebra and Logic

Discrete Mathematics

Mathematical Analysis

Identifiers

DOI

10.4310/MRL.2021.v28.n2.a7

More information

Latest update

6/18/2021