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Tenth order mock theta functions in Ramanujan's lost notebook (IV)
Author(s):
Youn-Seo
Choi
Journal:
Trans. Amer. Math. Soc.
354
(2002),
705-733.
MSC (2000):
Primary 11B65;
Secondary 11F20, 33E05
Posted:
September 21, 2001
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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.
References:
-
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- G. E. Andrews and D. Hickerson, Ramanujan's "Lost" Notebook VII:The sixth order mock theta functions, Adv. Math. 89 (1991), 60-105. MR 92i:11027
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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:
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
Posted:
September 21, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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