Every Real Algebraic Integer Is a Difference of Two Mahler Measures

• Autores: Paulius Drungilas, Arturas Dubickas
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 2, 2007, págs. 191-195
• Idioma: inglés
• DOI: 10.4153/cmb-2007-020-0
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• Resumen

  • 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(P) - bM(Q) with irreducible polynomials P, Q \in (mathbb Z)[X] of degree d and a positive integer b. Finally, if d leqslant 3, then one can take b = 1