منابع مشابه
Perspectives 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
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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....
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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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Article history: Received 22 August 2013 Accepted 20 December 2013 Available online 17 January 2014 Communicated by George E. Andrews MSC: 11P82 11P84 11F37 11F50 33D15
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Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.02.001