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

Title
On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5
Authors
Eum, Ick SunJung, Ho Yun
Ewha Authors
정호윤
Issue Date
2019
Journal Title
OPEN MATHEMATICS
ISSN
2391-5455JCR Link
Citation
OPEN MATHEMATICS vol. 17, pp. 1631 - 1651
Keywords
modular formsmodular tracesGalois tracesclass field theory
Publisher
SCIENDO
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
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.
DOI
10.1515/math-2019-0115
Appears in Collections:
ETC > ETC
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