Quantum modular forms and Hecke operators
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It is known that there are one-to-one correspondences 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.
KeywordsModular form Quantum modular form Dedekind symbol Period polynomial Hecke operator
This is part of the author’s undergraduate thesis paper. The author is grateful to the advisor Y. Choie for her helpful advice. The author is also grateful to S. Fukuhara, D. Choi and K. Ono for their comments via emails and J. Baek for his help about SAGE codes.
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