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.
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Jeon, D., Kang, SY. & Kim, C.H. Modularity of Galois traces of class invariants. Math. Ann. 353, 37–63 (2012). https://doi.org/10.1007/s00208-011-0671-2
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DOI: https://doi.org/10.1007/s00208-011-0671-2