On Ramanujan's definition of mock theta function
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...
متن کاملTransformation Formula of the “2nd” Order Mock Theta Function
KAZUHIRO HIKAMI A. We give a transformation formula for the " 2nd order " mock theta function D 5 (q) = ∞ n=0 (−q) n (q; q 2) n+1 q n which was recently proposed in connection with the quantum invariant for the Seifert manifold.
متن کاملOn Two Fifth Order Mock Theta Functions
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.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2013
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1301046110