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

Takashi Fukuda; Naoki Kanayama; Keiichi Komatsu

doi:10.1017/S0305004106009248

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

Takashi Fukuda, Naoki Kanayama, Keiichi Komatsu

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Abstract

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

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	141
Issue number	1
DOIs	https://doi.org/10.1017/S0305004106009248
Publication status	Published - 2006 Jul

ASJC Scopus subject areas

Mathematics(all)

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

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