On the mock-theta behavior of Appell–Lerch series
نویسندگان
چکیده
منابع مشابه
On Ramanujan's definition of mock theta function.
In his famous "deathbed" letter, Ramanujan "defined" the notion of a mock theta function and offered some examples of functions he believed satisfied his definition. Very recently, Griffin et al. established for the first time that Ramanujan's mock theta functions actually satisfy his own definition. On the other hand, Zwegers' 2002 doctoral thesis [Zwegers S (2002) Mock theta functions. PhD th...
متن کاملRamanujan's mock theta functions.
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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We consider the fifth order mock theta functions χ0 and χ1, defined by Ramanujan, and find identities for these functions, which relate them to indefinite theta functions. Similar identities have been found by Andrews for the other fifth order mock theta functions and the seventh order functions.
متن کاملThe Tenth Order Mock Theta Functions Revisited
In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan’s lost notebook. These were originally proved by Choi. Here we give an alternative proof.
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Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain c...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2015
ISSN: 1631-073X
DOI: 10.1016/j.crma.2015.09.028