On Siegel invariants of certain CM-fields

On Siegel invariants of certain CM-fields

We first construct Siegel invariants of some CM-fields in terms of special values of theta constants, which would be a generalization of Siegel–Ramachandra invariants of imaginary quadratic fields. We further describe Galois actions on these invariants and provide a numerical example to show that th...

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Veröffentlicht in:The Ramanujan journal 2021-02, Vol.54 (2), p.261-284
Hauptverfasser: Koo, Ja Kyung, Robert, Gilles, Shin, Dong Hwa, Yoon, Dong Sung
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fields (mathematics)
Fourier Analysis
Functions of a Complex Variable
Invariants
Mathematics
Mathematics and Statistics
Number Theory
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Beschreibung
Zusammenfassung:We first construct Siegel invariants of some CM-fields in terms of special values of theta constants, which would be a generalization of Siegel–Ramachandra invariants of imaginary quadratic fields. We further describe Galois actions on these invariants and provide a numerical example to show that this invariant really generates the ray class field of a CM-field.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-019-00223-3