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

Dohoon Choi; Daeyeol Jeon; Soon Yi Kang; Chang Heon Kim

doi:10.1016/j.jnt.2007.04.002

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

Dohoon Choi, Daeyeol Jeon, Soon Yi Kang, Chang Heon Kim

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	700-707
Number of pages	8
Journal	Journal of Number Theory
Volume	128
Issue number	3
DOIs	https://doi.org/10.1016/j.jnt.2007.04.002
Publication status	Published - 2008 Mar
Externally published	Yes

Keywords

Modular functions of prime level p
Trace of singular moduli

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2007.04.002

Cite this

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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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AU - Choi, Dohoon

AU - Jeon, Daeyeol

AU - Kang, Soon Yi

AU - Kim, Chang Heon

PY - 2008/3

Y1 - 2008/3

N2 - 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.

AB - 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.

KW - Modular functions of prime level p

KW - Trace of singular moduli

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DO - 10.1016/j.jnt.2007.04.002

M3 - Article

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EP - 707

JO - Journal of Number Theory

JF - Journal of Number Theory

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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