Let Î± be an algebraic integer of degree d, not 0 or a root of unity, all of whose conjugates Î±i are confined to a sector | arg z| â‰¤ Î¸. In the paper On the absolute Mahler measure of polynomialsâ€¦ (More)

In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in C give very good bounds for coefficients of polynomials with small Mahler measure. Byâ€¦ (More)

The house of an algebraic integer of degree d is the largest modulus of its conjugates. For d â‰¤ 28, we compute the smallest house > 1 of degree d, say m(d). As a consequence we improve Matveevâ€™sâ€¦ (More)

We determine the minimal Mahler measure of a primitive, irreducible, noncyclotomic polynomial with integer coefficients and fixed degree D, for each even degree D â‰¤ 54. We also compute all primitive,â€¦ (More)

We find all 15909 algebraic integers whose conjugates all lie in an ellipse with two of them nonreal, while the others lie in the real interval [âˆ’1, 2]. This problem has applications to findingâ€¦ (More)

Let Î± be an algebraic integer of degree d, not 0 or a root of unity, all of whose conjugates Î±i lie in a sector | arg z| â‰¤ Î¸. In 1995, G. Rhin and C. Smyth computed the greatest lower bound c(Î¸) ofâ€¦ (More)

We prove that, for any unit in a real number fieldK of degree n+ 1, there exits only a finite number of n-tuples in K which have a purely periodic expansion by the Jacobi-Perron algorithm. Thisâ€¦ (More)