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