Asymptotic expansions, L-values and a new Quantum Modular Form

2013/11/14 by Edgar Costa, Costa, Edgar, Korneel Debaene +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.3469

openalex publication_date 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function F(q) of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of F(q).

Citations

• The Final Problem : An Account of the Mock Theta Functions

Related

• Renormalization and quantum modular forms, part II: Mock theta functions
• Renormalization and quantum modular forms, part I: Maass wave forms
• Antiquantum q-series and mock theta functions
• Alternating "strange" functions
• Quantum mock modular forms arising from eta-theta functions