Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
نویسندگان
چکیده
منابع مشابه
q-HYPERGEOMETRIC DOUBLE SUMS AS MOCK THETA FUNCTIONS
Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums. Additionally, we prove an identity between one of these sums and two classical mock theta functions introduced by Gordon and McIntosh.
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In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2014
ISSN: 0024-6115
DOI: 10.1112/plms/pdu007