Elsevier

Journal of Number Theory

Volume 80, Issue 2, February 2000, Pages 260-272
Journal of Number Theory

Regular Article
A Lower Bound for the Height in Abelian Extensions

https://doi.org/10.1006/jnth.1999.2451Get rights and content
Under an Elsevier user license
open archive

Abstract

We produce an absolute lower bound for the height of the algebraic numbers (different from zero and from the roots of unity) lying in an abelian extension of the rationals. The proof rests on elementary congruences in cyclotomic fields and on Kronecker–Weber theorem.

Cited by (0)

Communicated by M. Waldschmidt