Bilateral Two-Parameter Mock Theta Functions and Related Applications

2025/10/16 by Wang, Chun
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.15185

Abstract

In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the classical mock theta functions and the bilateral series are also concluded.

Citations

• Automatic Proof of Theta-Function Identities
• On the dual nature of partial theta functions and Appell–Lerch sums
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• The H and K Family of Mock Theta Functions
• Dyson’s ranks and Maass forms
• Mock Jacobi forms in basic hypergeometric series
• Sixth order mock theta functions
• Second Order Mock Theta Functions
• Some Eighth Order Mock Theta Functions
• Ramanujan's “lost” notebook VII: The sixth order mock theta functions
• The Final Problem : An Account of the Mock Theta Functions

Related

• A Comprehensive Study of Complete Generalized New Mock Theta Functions
• Second Order Mock Theta Functions
• New fifth and seventh order mock theta function identities
• Representations of mock theta functions
• Further results on Andrews--Yee's two identities for mock theta functions ω(z;q) and v(z;q)