منابع مشابه
Proof of the umbral moonshine conjecture
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay–Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here, we establish the existence of the umbral moonshine modules in the remaining 22 cases. Mathematics ...
متن کاملMIXED MOCK MODULAR q-SERIES
Mixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common than mock theta functions. In this survey, we discuss some of the ways such series arise.
متن کاملPerspectives on mock modular forms
Article history: Received 30 August 2016 Received in revised form 2 February 2017 Accepted 20 February 2017 Available online 24 February 2017 Communicated by D. Goss
متن کاملHarmonic Maass Forms, Mock Modular Forms, and Quantum Modular Forms
This short course is an introduction to the theory of harmonic Maass forms, mock modular forms, and quantum modular forms. These objects have many applications: black holes, Donaldson invariants, partitions and q-series, modular forms, probability theory, singular moduli, Borcherds products, central values and derivatives of modular L-functions, generalized Gross-Zagier formulae, to name a few....
متن کاملMOCK MODULAR FORMS AS p-ADIC MODULAR FORMS
In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.
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ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2015
ISSN: 2197-9847
DOI: 10.1186/s40687-015-0034-9