Showing math.NTShow all
3 papers · 1 filter
math.NT2023
On a new absolute version of Siegel's lemma
Maxwell Forst, Lenny Fukshansky
We establish a new version of Siegel's lemma over a number field , providing a bound on the maximum of heights of basis vectors of a subspace of , . In addition t…
math.NT2022
On zeros of multilinear polynomials
Maxwell Forst, Lenny Fukshansky
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove…
math.NT2020
Counting basis extensions in a lattice
Maxwell Forst, Lenny Fukshansky
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by , producing an asym…