P. Gruber

collaborators

3 papers

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

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…