Circular units of abelian fields with a prime power conductor
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For an abelian extension K of Q, let CW(K) be the group of Washington units of K, and CS(K) the group of Sinnott units of K. A lot of results about CS(K) have been found while very few is known about CW(K). This is mainly because elements in CS(K) are more explicitly defined than those in CW(K). The aim of this paper is to find a basis of CW(K) and use it to compare CW(K) and CS(K) when K is a subfield of Q(ζpe), where p is a prime.
Abstract
For an abelian extension K of Q, let CW(K) be the group of Washington units of K, and CS(K) the group of Sinnott units of K. A lot of results about CS(K) have been found while very few is known about CW(K). This is mainly because elements in CS(K) are more explicitly defined than those in CW(K). The aim of this paper is to find a basis of CW(K) and use it to compare CW(K) and CS(K) when K is a subfield of Q(ζpe), where p is a prime.
참고문헌 (5)
- C. Greither, "Uber relativ-invariante Kreiseinheiten und Stickelberger-Elemente", Manuscripta Math., 80, pp.27~43 (1993)
- R. Kucera, "On the Stickelberger ideal and circular units of some genus fields", Tatra Mt. Math. Publ., 20, pp.93~104 (2000)
- W. Sinnott, "On the Stickelberger ideal and the circular units of a cyclo-tomic field", Ann. of Math. (2), 108, pp.107~134 (1978)
- W. Sinnott, "On the Stickelberger ideal and the circular units of an abelian field", Invent. Math., 62, pp.181~234 (1980)
- L. Washington, "Introduction to Cyclotomic Fields" (1980), Springer-Verlag