Article contents
Every Real Algebraic Integer Is a Difference of Two Mahler Measures
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove that every real algebraic integer $\alpha$ is expressible by a difference of two Mahler measures of integer polynomials. Moreover, these polynomials can be chosen in such a way that they both have the same degree as that of
$\alpha$, say
$d$, one of these two polynomials is irreducible and another has an irreducible factor of degree
$d$, so that
$\alpha =M\left( P \right)-bM\left( Q \right)$ with irreducible polynomials
$P,Q\in \mathbb{Z}\left[ X \right]$ of degree
$d$ and a positive integer
$b$. Finally, if
$d\le 3$, then one can take
$b=1$.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2007
References
- 1
- Cited by