Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
Choi, Youn-Seo
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https://hdl.handle.net/2142/86972
Description
Title
Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
Author(s)
Choi, Youn-Seo
Issue Date
1999
Doctoral Committee Chair(s)
Berndt, Bruce C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions which heretofore have not been proved. It is the purpose of this thesis to prove the first four of Ramanujan's tenth order mock theta function identities. Although in this paper the Bailey pair method developed by G. E. Andrews and the constant term method developed by D. Hickerson are playing key roles, the other main idea is transforming mock theta function identities into the theta function identities.
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