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Exact formulas for traces of singular moduli of higher level modular functions

Dohoon Choi·Daeyeol Jeon·Soon-Yi Kang·Chang Heon Kim
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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.

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Dohoon Choi, Daeyeol Jeon, Soon-Yi Kang, Chang Heon Kim. 2007-01-31. Exact formulas for traces of singular moduli of higher level modular functions. https://arxiv.org/abs/math/0701908

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