Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms
Artikel i vetenskaplig tidskrift, 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.


Michael H. Mertens

University of Liverpool

Martin Raum

Chalmers, Matematiska vetenskaper, Algebra och geometri

Mathematical Research Letters

1073-2780 (ISSN) 1945001x (eISSN)

Vol. 28 2 511-561


Algebra och logik

Diskret matematik

Matematisk analys



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