Indecomposable vector-valued modular forms and periods of modular curves

Candelori, Luca; Hartland, Tucker; Marks, Christopher; Diego, Yepez,

doi:10.48550/arxiv.1707.01693

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2017

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“…(5) Apparently unaware of either [BK13] or its rephrasing in terms of vector-valued modular forms, the authors of [Can+17] reproduce [BK13] in their Theorem 1.4. It is also a special case of our Proposition 3.15.…”

Section: Theorem I Let F Bementioning

confidence: 99%

Modular forms of virtually real-arithmetic type I -- Mixed mock modular forms yield vector-valued modular forms

Mertens,

Raum

2017

Preprint

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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 2 (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.vector-valued modular forms mixed mock modular forms higher order modular forms iterated Eichler-Shimura integrals Hecke operators Eisenstein series Poincaré series

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Section: Theorem I Let F Bementioning

confidence: 99%