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Modularity of Galois traces of ray class invariants

Title
Modularity of Galois traces of ray class invariants
Authors
Jung, Ho YunKim, Chang Heon
Ewha Authors
정호윤
Journal Title
RAMANUJAN JOURNAL
ISSN
1382-4090JCR Link

1572-9303JCR Link
Citation
RAMANUJAN JOURNAL
Keywords
Modular formsModular tracesGalois tracesClass field theory
Publisher
SPRINGER
Indexed
SCIE; SCOPUS WOS
Document Type
Article

Early Access
Abstract
After Zagier's significant work (in: Bogomolov and Katzarkov (eds) Motives, polylogarithms and hodge theory, part I, International Press, Somerville, 2002) on traces of singular moduli, Bruinier and Funke (J Reine Angew Math 594:1-33, 2006) generalized his result to the traces of singular values of modular functions on modular curves of arbitrary genus. In class field theory, the extended ring class field is a generalization of the ray class field over an imaginary quadratic field. By using Shimura's reciprocity law, we construct primitive generators of the extended ring class fields by using Siegel functions of arbitrary level N >= 2 and identify their Galois traces with Fourier coefficients of weight 3/2 harmonic weak Maass forms. This would extend the results of Jeon et al. (Math Ann 353:37-63, 2012) and Jung et al. (Modularity of Galois traces of Weber's resolvents, under revision).
DOI
10.1007/s11139-019-00220-6
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연구기관 > 수리과학연구소 > Journal papers
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