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

Edgar Costa; Korneel Debaene; João Guerreiro

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

Number Theory 2013-11-15 v1

Authors: Edgar Costa , Korneel Debaene , João Guerreiro

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

modular forms asymptotic analysis

Cite

@article{arxiv.1311.3469,
  title  = {Asymptotic expansions, $L$-values and a new Quantum Modular Form},
  author = {Edgar Costa and Korneel Debaene and João Guerreiro},
  journal= {arXiv preprint arXiv:1311.3469},
  year   = {2013}
}

Comments

7 pages

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