Metric heights are modified height functions on the non-zero algebraic numbers Q âˆ— which can be used to define a metric on certain cosets of Q âˆ— . They have been defined with a view to eventuallyâ€¦ (More)

We show that the number of distinct non-parallel lines passing through two conjugates of an algebraic number Î± of degree d 3 is at most [d2/2] âˆ’ d + 2, its conjugates being in general position ifâ€¦ (More)

We consider the sequence of fractional parts {Î¾Î±n}, n = 1, 2, 3, . . . , where Î± > 1 is a Pisot number and Î¾ âˆˆ Q(Î±) is a positive number. We find the set of limit points of this sequence and describeâ€¦ (More)

In fact, Schneider 's method was used in the proof, but replacement of Siegel ' s l e m m a by Laurent ' s interpolation determinant led to the relatively small numerical constant c = 1 + e, where eâ€¦ (More)

Applicable Algebra in Engineering, Communicationâ€¦

2003

We compute the probability for a monic univariate integer polynomial to be irreducible by Eisenstein's Criterion. In particular, it follows that less than 1% of the polynomials with at least sevenâ€¦ (More)

We investigate the connection between the degree of an algebraic number over a field of characteristic zero and the degree of a linear form in its conjugates. Special attention is given to the caseâ€¦ (More)

Recall that a polynomial P (x) âˆˆ Z[x] with coefficients 0, 1 and constant term 1 is called a Newman polynomial, whereas a polynomial with coefficients âˆ’1, 1 is called a Littlewood polynomial. Isâ€¦ (More)

For all but one positive integer triplet (a, b, c) with a 6 b 6 c and b 6 6, we decide whether there are algebraic numbers Î±, Î² and Î³ of degrees a, b and c, respectively, such that Î±+Î²+ Î³ = 0. Theâ€¦ (More)