## Journal of the Mathematical Society of Japan

### Distribution of units of a cubic abelian field modulo prime numbers

Yoshiyuki KITAOKA

#### Abstract

We studied the distribution of units of an algebraic number field modulo prime ideals. Here we study the distribution of units of a cubic abelian field modulo rational prime numbers. For a decomposable prime number $p$, $2(p-1)^2$ is an upper bound of the order of the unit group modulo $p$, and we show that the conjectural density of primes which attain it is really positive.

#### Article information

Source
J. Math. Soc. Japan, Volume 58, Number 2 (2006), 563-584.

Dates
First available in Project Euclid: 1 June 2006

https://projecteuclid.org/euclid.jmsj/1149166789

Digital Object Identifier
doi:10.2969/jmsj/1149166789

Mathematical Reviews number (MathSciNet)
MR2228573

Zentralblatt MATH identifier
1108.11080

Subjects
Primary: 11R27: Units and factorization

#### Citation

KITAOKA, Yoshiyuki. Distribution of units of a cubic abelian field modulo prime numbers. J. Math. Soc. Japan 58 (2006), no. 2, 563--584. doi:10.2969/jmsj/1149166789. https://projecteuclid.org/euclid.jmsj/1149166789

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