FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS - Kölner UniversitätsPublikationsServer

Andrews, George E., Berndt, Bruce C., Chan, Song Heng ORCID: 0000-0002-3696-2768, Kim, Sun and Malik, Amita (2020). FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS. Nagoya Math. J., 239. S. 173 - 205. NEW YORK: CAMBRIDGE UNIV PRESS. ISSN 2152-6842

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DOI:10.1017/nmj.2018.35

Abstract

In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3)4(1954), 84-106), Yesilyurt (Four identities related to third order mock theta functions in Ramanujan's lost notebook, Adv. Math. 190(2005), 278-299) proved four identities for third order mock theta functions found on pages 2 and 17 in Ramanujan's lost notebook. The primary purpose of this paper is to offer new proofs in the spirit of what Ramanujan might have given in the hope that a better understanding of the identities might be gained. Third order mock theta functions are intimately connected with ranks of partitions. We prove new dissections for two rank generating functions, which are keys to our proof of the fourth, and the most difficult, of Ramanujan's identities. In the last section of this paper, we establish new relations for ranks arising from our dissections of rank generating functions.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Andrews, George E.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Berndt, Bruce C.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Chan, Song Heng	UNSPECIFIED	orcid.org/0000-0002-3696-2768	UNSPECIFIED
Kim, Sun	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Malik, Amita	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED