5 papers · 1 filter
Integer Knapsacks: Average Behavior of the Frobenius Numbers
Iskander Aliev, Martin Henk
The main result of the paper shows that the asymptotic growth of the Frobenius number in average is significantly slower than the growth of the maximum Frobenius number.
Power maps and subvarieties of the complex algebraic --torus
Iskander Aliev, Chris Smyth
Given a subvariety of the complex algebraic torus defined by polynomials of total degree at most and a power map $ϕ: {\mathbb G}_{\rm m}^n \to {\mat…
Solving algebraic equations in roots of unity
Iskander Aliev, Chris Smyth
This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be describe…
Successive Minima and Best Simultaneous Diophantine Approximations
Iskander Aliev, Martin Henk
We study the problem of best approximations of a vector by rational vectors of a lattice whose common denominator is bounded. To this e…
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…