Asymptotic expansions, L-values and a new quantum modular form
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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).
KeywordsMock theta function Quantum modular form
Mathematics Subject Classification (2000)11F37 11F67
We would like to thank professors Ken Ono and Rob C. Rhoades for bringing this problem to our attention. We would also like to thank the Arizona Winter School for creating opportunities for research and providing an excellent platform for collaboration.
- 2.Chern, B., Rhoades, R.C.: The Mordell integral and quantum modular forms (2012, preprint) Google Scholar
- 4.Folsom, A., Ono, K., Rhoades, R.C.: Ramanujan’s radial limits (2012, submitted for publication) Google Scholar
- 8.Zagier, D.: Quantum modular forms. In: Quanta of Maths. Clay Math. Proc., vol. 11, pp. 659–675. Am. Math. Soc., Providence (2010) Google Scholar
- 9.Zwegers, S.P.: Mock theta functions. Ph.D. Thesis (Advisor: D. Zagier), Universiteit Utrecht (2002) Google Scholar