English

Quantum modular forms and Hecke operators

Number Theory 2024-03-22 v3

Abstract

It is known that there is an one-to-one correspondence among the space of cusp forms, the space of homogeneous period polynomials and the space of Dedekind symbols with polynomial reciprocity laws. We add one more space, the space of quantum modular forms with polynomial period functions, to extend results from Fukuhara. Also, we consider Hecke operators on the space of quantum modular forms and construct new quantum modular forms.

Keywords

Cite

@article{arxiv.1706.05824,
  title  = {Quantum modular forms and Hecke operators},
  author = {Seewoo Lee},
  journal= {arXiv preprint arXiv:1706.05824},
  year   = {2024}
}

Comments

15 pages, corrected typos, added the Lemma 4.1 that helps us to find more examples using SAGE

R2 v1 2026-06-22T20:22:25.036Z