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Prime divisors of special values of theta functions in the ray class field of a certain quartic field modulo $2^n$

Published online by Cambridge University Press:  03 July 2006

TAKASHI FUKUDA
Affiliation:
Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan. e-mail: fukuda@math.cit.nihon-u.ac.jp
NAOKI KANAYAMA
Affiliation:
Department of Information and Comunication Engineering, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-shi, Tokyo, 182-8585 Japan. e-mail: kanayama@ice.uec.ac.jp
KEIICHI KOMATSU
Affiliation:
Department of Mathematical Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan. e-mail: kkomatsu@mse.waseda.ac.jp

Abstract

We construct certain algebraic integers $\alpha_n$ as special values of two variable theta functions in the ray class field of a certain quartic field modulo $2^n$, and study a property of prime ideals which appear in $\alpha_n$ in connection to the relationships between cyclotomic units and exponential functions and between elliptic units and elliptic theta functions.

Type
Research Article
Copyright
2006 Cambridge Philosophical Society

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