## Duke Mathematical Journal

### The asymptotic distribution of traces of cycle integrals of the $j$-function

#### Abstract

We establish an asymptotic formula with a power savings in the error term for traces of cycle integrals of the classical modular $j$-function

$$j(z)=q^{-1}+744+196884q+21493760q^{2}+\cdots.$$

This implies a conjecture of Duke, Imamoḡlu, and Tóth.

#### Article information

Source
Duke Math. J., Volume 161, Number 10 (2012), 1971-2000.

Dates
First available in Project Euclid: 27 June 2012

https://projecteuclid.org/euclid.dmj/1340801629

Digital Object Identifier
doi:10.1215/00127094-1645711

Mathematical Reviews number (MathSciNet)
MR2954622

Zentralblatt MATH identifier
1287.11060

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms
Secondary: 11L15: Weyl sums

#### Citation

Masri, Riad. The asymptotic distribution of traces of cycle integrals of the $j$ -function. Duke Math. J. 161 (2012), no. 10, 1971--2000. doi:10.1215/00127094-1645711. https://projecteuclid.org/euclid.dmj/1340801629

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