SIGNATURE RANKS OF UNITS IN CYCLOTOMIC EXTENSIONS OF ABELIAN NUMBER FIELDS

被引：4

作者：

Dummit, David S. ^{[1
]}

Dummit, Evan P. ^{[2
]}

Kisilevsky, Hershy ^{[3
]}

机构：

[1] Univ Vermont, Dept Math, Burlington, VT 05405 USA

[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ USA

[3] Concordia Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2019年 / 298卷 / 02期

关键词：

signature rank of units; cyclotomic fields; abelian extensions; circular units;

D O I：

10.2140/pjm.2019.298.285

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the rank of the group of signatures of the circular units (hence also the full group of units) of Q(zeta(m))(+) tends to infinity with m. We also show the signature rank of the units differs from its maximum possible value by a bounded amount for all the real subfields of the composite of an abelian field with finitely many odd prime-power cyclotomic towers. In particular, for any prime p the signature rank of the units of Q(zeta(pn))(+) differs from phi(p(n))/2 by an amount that is bounded independent of n. Finally, we show conditionally that for general cyclotomic fields the unit signature rank can differ from its maximum possible value by an arbitrarily large amount.

引用

页码：285 / 298

页数：14