On the Mahler measure of the composition of two polynomials

ArticleOriginal scientific text

Title

Authors ¹, ²

URA CNRS no.399, Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 1, France
Department of Mathematics and Statistics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, UK

[BeZa] F. Beukers and D. Zagier, Lower bounds of heights of points on hypersurfaces, this volume, 103-111.
[BlMo] P. E. Blanksby and H. L. Montgomery, Algebraic integers near the unit circle, Acta Arith. 18 (1971), 355-369.
[Ca] J. W. S. Cassels, On a problem of Schinzel and Zassenhaus, J. Math. Sci. 1 (1966), 1-8.
[Do] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401.
[Fl1] V. Flammang, Sur la longueur des entiers algébriques totalement positifs, J. Number Theory 54 (1995), 60-72.
[Fl2] V. Flammang, Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers, Math. Comp. 65 (1996), 307-311.
[RhSm] G. Rhin and C. Smyth, On the absolute Mahler measure of polynomials having all zeros in a sector, Math. Comp. 64 (1995), 295-304.
[ScZas] A. Schinzel and H. Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965), 81-84.
[Si] C. L. Siegel, The trace of totally positive and real algebraic integers, Ann. of Math. 46 (1965), 302-312.
[Sm1] C. J. Smyth, On the measure of totally real algebraic integers II, Math. Comp. 37 (1981), 205-208.
[Sm2] C. J. Smyth, The mean values of totally real algebraic integers, Math. Comp. 42 (1984), 663-681.
[Za] D. Zagier, Algebraic numbers close to both 0 and 1, Math. Comp. 61 (1993), 485-491.
[Zh] S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. (2) 136 (1992), 569-587.