WebHickerson [5] gave Hecke-type double sums for the sixth order mock theta functions. Around 2000, Choi [8,9] discussed the tenth order mock theta functions. Moreover, Hecke-type double sums for the third order mock theta functions are found in [3,7, 10,14,17]. The first object of this paper is to establish Hecke-type double sums for Web1 jul. 2015 · unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q -hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z.
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Webexamples of q-hypergeometric series which are mock theta functions (in the modern sense). Date: July 25, 2012. 2010 Mathematics Subject Classi cation. ... for Joyce invariants [35], in the quantum theory of black holes and wall-crossing phenomenon [26], in … Web11 apr. 2024 · 3 Generalized A2 False Theta Functions 14 ... This structure has played a role in the gravitational black hole interpreta-tion of the BPS indices in the context of AdS3/CFT2 [15–18] and AdS2/CFT1 ... false [24,35,36] and mock theta functions [24,30,37,38] have been proposed. Generally, we git clone without making folder
Almost a Century of Answering the Question: What Is a Mock …
WebRamanujan, Mock theta, black hole, ramanujan, indian mathematician ramanujan, ramanujan tricks, tricky mathematics Webmock 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. WebThe quantum degeneracies of single-centered black holes are Fourier coefficients of this mock Jacobi form, while the Appell-Lerch sum captures the degeneracies of multi-centered black holes which decay upon wall-crossing. git clone without remote origin