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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tenth order mock theta functions in Ramanujan's lost notebook (IV)


Author: Youn-Seo Choi
Journal: Trans. Amer. Math. Soc. 354 (2002), 705-733
MSC (2000): Primary 11B65; Secondary 11F20, 33E05
Published electronically: September 21, 2001
MathSciNet review: 1862564
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Abstract: Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved the first six of Ramanujan's tenth order mock theta function identities. It is the purpose of this paper to prove the seventh and eighth identities of Ramanujan's tenth order mock theta function identities which are expressed by mock theta functions and a definite integral. L. J. Mordell's transformation formula for the definite integral plays a key role in the proofs of these identities. Also, the properties of modular forms are used for the proofs of theta function identities.


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Additional Information

Youn-Seo Choi
Affiliation: Department of Mathematics, Korea University, 5-1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea
Email: y-choi2@mail.korea.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02861-6
PII: S 0002-9947(01)02861-6
Keywords: Ramanujan, definite integral, theta function, mock theta function
Received by editor(s): August 11, 2000
Published electronically: September 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society