ON THE TENTH-ORDER MOCK THETA FUNCTIONS

2016/09/30 by Eric T. Mortenson · 10 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Analytic Number Theory Research #Geometry #Mathematical proof #Mathematics #Order (exchange) #Pure mathematics #Ramanujan theta function #Ramanujan's sum #math.NT

paper · pdf · doi:10.1017/s1446788717000015

published in Journal of the Australian Mathematical Society 104(1), 44-62 (Cambridge University Press) · 18 pages. New proofs for identities (2.11) and (2.12)

arxiv created 2016/10/09 · openalex publication_date 2017/03/02 · arxiv updated 2018/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using properties of Appell–Lerch functions, we give insightful proofs for six of Ramanujan’s identities for the tenth-order mock theta functions.

Citations

• The Mock Theta Functions (2)
• The Final Problem : An Account of the 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
• Dyson’s ranks and Maass forms
• A proof of the mock theta conjectures
• Tenth order mock theta functions in Ramanujan's lost notebook III
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Tenth order mock theta functions in Ramanujan's Lost Notebook