A proof of the mock theta conjectures
type: Item
instance of: scholarly article
title: A proof of the mock theta conjectures
zbMATH Open document ID: 0661.10059
DOI: 10.1007/BF01394279
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143640
review text: In his ``lost'' notebook, Ramanujan stated identities involving each of the ten fifth order mock theta functions, which he divided into two groups. \textit{G. E. Andrews} and \textit{F. G. Garvan} [Ramanujan's ``Lost'' Notebook VI: The mock theta conjectures; Adv. Math. 73, No.2, 242-255 (1989)] showed that these identities are all equivalent to two identities, which they call the first and second mock theta conjectures (one conjecture for each group of mock theta functions). The author proves both of these conjectures. The proof relies on a pair of Hecke type identities discovered by \textit{G. E. Andrews} [Trans. Am. Math. Soc. 293, 113-134 (1986; Zbl 0593.10018)].
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 4079555
zbMATH Keywords: fifth order mock theta functions
zbMATH Keywords: identities
zbMATH Keywords: mock theta conjectures
zbMATH Keywords: Hecke type identities
Wikidata QID: Q64013568
author: Dean R. Hickerson
MaRDI profile type: Publication
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OpenAlex ID: W2092257726
description: scientific article; zbMATH DE number 4079555