Construction of class fields over cyclotomic fields

Let l and p be odd primes. For a positive integer mu, let k(mu), be the ray class field of k = Q(e(2 pi i/l)) modulo 2p(mu). We present certain class fields K-mu, of k such that k(mu) subset of K mu subset of k(mu+1), and we provide a necessary and sufficient condition for K-mu = k(mu+1). We also construct, in the sense of Hilbert, primitive generators of the field K-mu over k(mu) by using Shimura's reciprocity law and special values of theta constants.
Publisher
DUKE UNIV PRESS
Issue Date
2016-12
Language
ENG
Keywords

COMPLEX MULTIPLICATION; EXTENSIONS; VALUES

Citation

KYOTO JOURNAL OF MATHEMATICS, v.56, no.4, pp.803 - 829

ISSN
2156-2261
DOI
10.1215/21562261-3664923
URI
http://hdl.handle.net/10203/214560
Appears in Collection
MA-Journal Papers(저널논문)
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