Comments on the height reducing property II
No Thumbnail Available
Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
A complex number α is said to satisfy the height reducing property if there is a finite set F ⊂ Z such
that Z[α] = F[α], where Z is the ring of the rational integers. It is easy to see that α is an algebraic number
when it satisfies the height reducing property. We prove the relation Card(F) ≥ max{2, |Mα(0)|}, where
Mα is the minimal polynomial of α over the field of the rational numbers, and discuss the related optimal
cases, for some classes of algebraic numbers α. In addition, we show that there is an algorithm to determine
the minimal height polynomial of a given algebraic number, provided it has no conjugate of modulus one.
⃝c 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
Description
Keywords
Height of polynomials, Special algebraic numbers, Number systems