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

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

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