Exact formulas for traces of singular moduli of higher level modular functions
Number Theory
2007-05-23 v1
Abstract
Zagier proved that the traces of singular values of the classical j-invariant are the Fourier coefficients of a weight 3/2 modular form and Duke provided a new proof of the result by establishing an exact formula for the traces using Niebur's work on a certain class of non-holomorphic modular forms. In this short note, by utilizing Niebur's work again, we generalize Duke's result to exact formulas for traces of singular moduli of higher level modular functions.
Keywords
Cite
@article{arxiv.math/0701908,
title = {Exact formulas for traces of singular moduli of higher level modular functions},
author = {Dohoon Choi and Daeyeol Jeon and Soon-Yi Kang and Chang Heon Kim},
journal= {arXiv preprint arXiv:math/0701908},
year = {2007}
}
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8 pages