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The Ramanujan Journal

, Volume 35, Issue 1, pp 141–148 | Cite as

Asymptotic expansions, L-values and a new quantum modular form

  • Edgar Costa
  • Korneel Debaene
  • João Guerreiro
Article

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).

Keywords

Mock theta function Quantum modular form 

Mathematics Subject Classification (2000)

11F37 11F67 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Vakgroep WiskundeGhent UniversityGentBelgium
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA

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