Steffen Loebrich

Affiliation: University of Cologne

Email: steffen.loebrich@gmx.de

Title Of Talk: Poincaré Series and Traces of Singular Moduli

Abstract: We write Fourier coefficients of certain weight $2$ Poincaré series recently investigated by Bringmann and Kane in terms of Faber polynomials of the $j$-function. By summing over CM-points of binary quadratic forms of negative discriminant, we can interpret traces of singular moduli in the context of almost holomorphic modular forms of weight $2$. This new setting allows us to find a different approach to explicit series expressions for traces of singular moduli.

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