Let and be odd primes. For a positive integer , let be the ray class field of modulo . We present certain class fields of such that , and we provide a necessary and sufficient condition for . We also construct, in the sense of Hilbert, primitive generators of the field over by using Shimura’s reciprocity law and special values of theta constants.
"Construction of class fields over cyclotomic fields." Kyoto J. Math. 56 (4) 803 - 829, December 2016. https://doi.org/10.1215/21562261-3664923