Modularity of Galois traces of class invariants

Abstract

Zagier showed that the Galois traces of the values of j-invariant at CM points are Fourier coefficients of a weakly holomorphic modular form of weight 3/2 and Bruinier-Funke expanded his result to the sums of the values of arbitrary modular functions at Heegner points. In this paper, we identify the Galois traces of real-valued class invariants with modular traces of the values of certain modular functions at Heegner points so that they are Fourier coefficients of weight 3/2 weakly holomorphic modular forms.