AbstractSuppose K is a field, αn∈K∗, and n is the least natural number with this property. We study the question on how many powers αj, 0⩽j<n, lie in a given K-linear space
For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ fo...
Let α be an algebraic number of degree d ≥ 2 over Q. Suppose for some pairwise coprime positive inte...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractWe show that the height of a nonzero algebraic number α that lies in an abelian extension of...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
AbstractRecently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metr...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
AbstractNew lower bounds are given for the sum of degrees of simple and distinct irreducible factors...
AbstractLet f(x) be a real valued polynomial in x of degree k⩾4 with leading coefficient α. In this ...
AbstractLet p be a prime k|p−1, t=(p−1)/k and γ(k,p) be the minimal value of s such that every numbe...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractWe study a non-linear minimization problem on H01(Ω)⊂Lq with q=2nn−2: inf‖u‖Lq=1∫Ω(1+|x|β|u|...
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent $\gamma_1, \d...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ fo...
Let α be an algebraic number of degree d ≥ 2 over Q. Suppose for some pairwise coprime positive inte...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractWe show that the height of a nonzero algebraic number α that lies in an abelian extension of...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
AbstractRecently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metr...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
AbstractNew lower bounds are given for the sum of degrees of simple and distinct irreducible factors...
AbstractLet f(x) be a real valued polynomial in x of degree k⩾4 with leading coefficient α. In this ...
AbstractLet p be a prime k|p−1, t=(p−1)/k and γ(k,p) be the minimal value of s such that every numbe...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractWe study a non-linear minimization problem on H01(Ω)⊂Lq with q=2nn−2: inf‖u‖Lq=1∫Ω(1+|x|β|u|...
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent $\gamma_1, \d...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ fo...
Let α be an algebraic number of degree d ≥ 2 over Q. Suppose for some pairwise coprime positive inte...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...