Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Choi, Youn-Seo

Contributors dc:contributor

• Berndt, Bruce C.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9944820

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86972