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).
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Acknowledgements
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.
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The first author was partially supported by FCT doctoral grant SFRH/BD/69914/2010. The second author was partially supported by the Fonds Professor Frans Wuytack. The third author was partially supported by FCT doctoral grant SFRH/BD/68772/2010.
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Costa, E., Debaene, K. & Guerreiro, J. Asymptotic expansions, L-values and a new quantum modular form. Ramanujan J 35, 141–148 (2014). https://doi.org/10.1007/s11139-013-9508-9
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DOI: https://doi.org/10.1007/s11139-013-9508-9