A note on units in cyclotomic fields
by
Juraj Kostra
University of Ostrava

Let K be a normal tamely ramified algebraic number field of degree n over the rationals Q. In 1974 Morris Newman [1] asked which rational integers are sums of two units from K in the case K is the p-th cyclotomic field. Let (p) be a prime ideal of rational integers Z, then any non-zero element from (p) is not a sum of two units from the p-th cyclotomic fields. In general any non-zero element from a prime ideal (p) is not a sum of two units for any field K in which the prime p is totally ramified. Moreover, if K is a cubic field then also p-1 is not a sum of two units from K.

1. M. Newman: Diophantine equations in cyclotomic fields. J. reine angew. Math. 265 (1974) 84-89

2. M. Newman: Units differing by rationals in cyclotomic field. Linear and Multilinear Algebra 34 (1993) 55-57

3. J. Kostra: On sums of two units. Abh. Math. Sem. Univ. Hamburg 64 (1994) 11-14

Date received: April 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-40.