Journal of the Mathematical Society of Japan

Distribution of units of a cubic abelian field modulo prime numbers

Yoshiyuki KITAOKA

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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

Permanent link to this document
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

Keywords
distribution of units cubic abelian field

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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References

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