Add to ORKGGiven a fixed number field K, we give non-trivial lower bounds for the distance between the conjugates of any number a from K in terms of the Mahler measure M(a) of a. In the case that K is a cubic field, our bound is best possible in terms of M(a). Our proof is based on Roth's theorem.Comment: Latex file; 18 page
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent $\gamma_1, \d...
AbstractLet Ap(D) (1⩽p<∞) be the Bergman space over the open unit disk D in the complex plane. For p...
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Let α be an algebraic number of degree d ≥ 2 over Q. Suppose for some pairwise coprime positive inte...
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Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent $\gamma_1, \d...
AbstractLet Ap(D) (1⩽p<∞) be the Bergman space over the open unit disk D in the complex plane. For p...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
Abstract. Let K be a given number field of degree r> 3, denote by ξ 7 → ξ(i) (i = 1,..., r) the i...
Let α be an algebraic number of degree d ≥ 2 over Q. Suppose for some pairwise coprime positive inte...
Let $\mathcal{A}$ and $\mathcal{B}$ be sets of polynomials of degree $n$ over a finite field. We sho...
AbstractLet f(x) be a real valued polynomial in x of degree k⩾4 with leading coefficient α. In this ...
In this paper, we show that if the sum ∑ r=1 ∞ Ψ(r) diverges, then the set of points (x, z, w) ∈ ℝ ×...
For all but one positive integer triplet (a; b; c) with a < b < c and b < 6, we decide whet...
AbstractFor the finite field Fp one may consider the distance between r1(n) and r2(n), where r1, r2 ...
A complex number αα is said to satisfy the height reducing property if there is a finite set F⊂ZF⊂Z ...
AbstractRecently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metr...
AbstractWe show that the distance between en and its nearest integer is estimated below by e−cnlogn ...
We establish a transference inequality conjectured by Badziahin and Bugeaud relating exponents of ra...
In the paper we obtain the lower bound for the number of polynomials with the absolute value of thei...
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent $\gamma_1, \d...
AbstractLet Ap(D) (1⩽p<∞) be the Bergman space over the open unit disk D in the complex plane. For p...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...