I. Aliev

activity

20052026

most citedSparse solutions of linear Diophantine equations

34 citations · 53 across the 24 of their papers we have counts for

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Showing 2005Show all

5 papers · 1 filter

math.NT2005

An Optimal Lower Bound for the Frobenius Problem

Iskander Aliev, Peter Gruber

Given $N$ positive integers $a_{1}, ..., a_{N}$ with $g cd (a_{1}, ..., a_{N}) = 1$ , let $f_{N}$ denote the largest natural number which is not a positive integer combination of $a_{1}, ..., a_{N}$ …

math.NT2005★ 1 cited

Best Simultaneous Diophantine Approximations under a Constraint on the Denominator

Iskander Aliev, Peter Gruber

We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximatio…

math.NT2005

Lattice Points in Large Borel Sets and Successive Minima

Iskander Aliev, Peter Gruber

Let $B$ be a Borel set in $E^{d}$ with volume $V (B) = \infty$ . It is shown that almost all lattices $L$ in $E^{d}$ contain infinitely many pairwise disjoint $d$ -tuple…

math.NT2005

Successive Minima and Best Simultaneous Diophantine Approximations

Iskander Aliev, Martin Henk

We study the problem of best approximations of a vector $α \in R^{n}$ by rational vectors of a lattice $Λ \subset R^{n}$ whose common denominator is bounded. To this e…

math.NT2005

Siegel's Lemma and Sum-Distinct Sets

Iskander Aliev

We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erdös-Moser…