The Fifth and Seventh Order Mock Theta Functions

1986/01/01 by George E. Andrews · 2 citations
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Mathematics #Modular form #Theta function #Ramanujan theta function #Type (biology) #Integer (computer science) #Order (exchange) #Generating function #Pure mathematics #Hecke operator #Series (stratigraphy) #Eisenstein series #Algebra over a field #Combinatorics

paper · pdf · doi:10.2307/2000275

openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The theory of Bailey chains is extended to yield identities for Hecke type modular forms and related generalizations. The extended results allow us to produce Hecke type series for the fifth and seventh order mock theta functions. New results on the generating function for sums of three squares also follow, and a new proof that every integer is the sum of three triangular numbers is given.

Citations

• On the Theorems of Watson and Dragonette for Ramanujan's Mock Theta Functions
• Second Memoir on the Expansion of certain Infinite Products
• Some Asymptotic Formulae for the Mock Theta Series of Ramanujan

Cited by

• The umbral moonshine module for the unique unimodular Niemeier root system
• Mock modular form [wikipedia]