Add to ORKGInternational audienceWe determine the true order of magnitude of the number of integers not exceeding x which have a prescribed number of divisors in a short interval, precisely defined in the text
For $d,k\in \mathbb{N}$ with $k\leq 2d$, let $g(d,k)$ denote the infimum density of binary sequences...
AbstractFor d,k∈N with k≤2d, let g(d,k) denote the infimum density of binary sequences (xi)i∈Z∈{0,1}...
AbstractFor the finite field Fp one may consider the distance between r1(n) and r2(n), where r1, r2 ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractWe show that the distance between en and its nearest integer is estimated below by e−cnlogn ...
We study higher uniformity properties of the M\"obius function $\mu$, the von Mangoldt function $\La...
We show that the expected asymptotic for the sums ∑_(X<n≤2X)Λ(n)Λ(n+h), ∑_(X<n≤2X)d_k(n)d_l(n+h), an...
AbstractThe main topic of the paper is best constants in Markov-type inequalities between the norms ...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
We modify the recent method of J.-M. Deshouillers and H. Iwaniec in the theory of uniform distributi...
Let $ d_k(n) $ denote the k-th divisor function. In this paper, we give the asymptotic formula of th...
AbstractWe study a non-linear minimization problem on H01(Ω)⊂Lq with q=2nn−2: inf‖u‖Lq=1∫Ω(1+|x|β|u|...
AbstractDenote am(n)=∑n1…nm=n;n1, …, nm⩾21 to be the number of ordered factorizations of an integer ...
For $d,k\in \mathbb{N}$ with $k\leq 2d$, let $g(d,k)$ denote the infimum density of binary sequences...
For $d,k\in \mathbb{N}$ with $k\leq 2d$, let $g(d,k)$ denote the infimum density of binary sequences...
AbstractFor d,k∈N with k≤2d, let g(d,k) denote the infimum density of binary sequences (xi)i∈Z∈{0,1}...
AbstractFor the finite field Fp one may consider the distance between r1(n) and r2(n), where r1, r2 ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractWe show that the distance between en and its nearest integer is estimated below by e−cnlogn ...
We study higher uniformity properties of the M\"obius function $\mu$, the von Mangoldt function $\La...
We show that the expected asymptotic for the sums ∑_(X<n≤2X)Λ(n)Λ(n+h), ∑_(X<n≤2X)d_k(n)d_l(n+h), an...
AbstractThe main topic of the paper is best constants in Markov-type inequalities between the norms ...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
We modify the recent method of J.-M. Deshouillers and H. Iwaniec in the theory of uniform distributi...
Let $ d_k(n) $ denote the k-th divisor function. In this paper, we give the asymptotic formula of th...
AbstractWe study a non-linear minimization problem on H01(Ω)⊂Lq with q=2nn−2: inf‖u‖Lq=1∫Ω(1+|x|β|u|...
AbstractDenote am(n)=∑n1…nm=n;n1, …, nm⩾21 to be the number of ordered factorizations of an integer ...
For $d,k\in \mathbb{N}$ with $k\leq 2d$, let $g(d,k)$ denote the infimum density of binary sequences...
For $d,k\in \mathbb{N}$ with $k\leq 2d$, let $g(d,k)$ denote the infimum density of binary sequences...
AbstractFor d,k∈N with k≤2d, let g(d,k) denote the infimum density of binary sequences (xi)i∈Z∈{0,1}...
AbstractFor the finite field Fp one may consider the distance between r1(n) and r2(n), where r1, r2 ...