Tenth order mock theta functions in Ramanujan's lost notebook III

2006/11/27 by Youn-Seo Choi · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics #Ramanujan's sum #Ramanujan theta function #Mathematics #Theta function #Order (exchange) #Ramanujan tau function #Mathematical proof #Modular form #Algebra over a field #Pure mathematics #Geometry

paper · doi:10.1112/plms/pdl006

openalex publication_date 2006/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06

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 six of the eight tenth order mock theta function identities. It is the purpose of this paper to prove the fifth and sixth identities of Ramanujan's tenth order mock theta functions. The properties of modular forms are used for the proofs of theta function identities.

Citations

• Tenth order mock theta functions in Ramanujan’s lost notebook (IV)
• On the seventh order mock theta functions
• Ramanujan's “lost” notebook VII: The sixth order mock theta functions
• Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook II
• A proof of the mock theta conjectures
• Tenth order mock theta functions in Ramanujan's Lost Notebook

Cited by

• ON THE TENTH-ORDER MOCK THETA FUNCTIONS
• Mock modular form [wikipedia]