P. Gruber

most citedBest Simultaneous Diophantine Approximations under a Constraint on the Denominator

1 citations · 1 across the 3 of their papers we have counts for

collaborators

4 papers

math.MG2012

An arithmetic proof of John's ellipsoid theorem

Peter M. Gruber, Franz E. Schuster

Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John's characterization of the unique ellipsoid of maximum vol…

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…