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On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

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Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of… Click to show full abstract

Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

Keywords: weber functions; galois traces; functions level; class invariants; generalized weber

Journal Title: Open Mathematics
Year Published: 2019

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