Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T10:54:25.922Z Has data issue: false hasContentIssue false
  • English
  • Français

COMPARISON OF MEASURES OF TOTALLY POSITIVE POLYNOMIALS

Published online by Cambridge University Press:  22 August 2013

V. FLAMMANG
V. FLAMMANG*
Affiliation:
UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université de Lorraine, site de Metz, Ile du Saulcy, 57045 METZ cedex 01, France email valerie.flammang@univ-lorraine.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, explicit auxiliary functions are used to get upper and lower bounds for the Mahler measure of monic irreducible totally positive polynomials with integer coefficients. These bounds involve the length and the trace of the polynomial.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 265 - 270
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Batut, C., Belabas, K., Bernardi, D., Cohen, H. and Olivier, M., ‘Pari/GP a software package for computer-aided number theory’. Available at http://www.math.u-psud.fr/belabas/pari/.Google Scholar
Flammang, V., ‘Comparaison de deux mesures de polynômes’, Canad. Math. Bull. 38 (4) (1995), 438–444.CrossRefGoogle Scholar
Flammang, V., ‘Sur la longueur des entiers algébriques totalement positifs’, J. Number Theory 54 (1) (1995), 60–72.Google Scholar
Flammang, V., ‘Trace of totally positive algebraic integers and integer transfinite diameter’, Math. Comp. 78 (266) (2009), 1119–1125.Google Scholar
Mignotte, M., Mathématiques Pour le Calcul Formel (Presses Universitaires de France, Paris, 1989).Google Scholar
Smyth, C. J., ‘On the measure of totally real algebraic integers I’, Math. Comp. 37 (1981), 205–208.Google Scholar
Smyth, C. J., ‘The mean value of totally real algebraic numbers’, Math. Comp. 42 (1984), 663–681.Google Scholar