24 citations · 55 across the 6 of their papers we have counts for
6 papers · 1 filter
On Mahler's inequality and small integral generators of totally complex number fields
Murray Child, Martin Widmer
We improve Mahler's lower bound for the Mahler measure in terms of the discriminant and degree for a specific class of polynomials: complex monic polynomials of degree su…
On a Counting Theorem of Skriganov
Niclas Technau, Martin Widmer
We prove a counting theorem concerning the number of lattice points for the dual lattices of weakly admissible lattices in an inhomogeneously expanding box, which generalises a cou…
On certain infinite extensions of the rationals with Northcott property
Martin Widmer
A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states…
Small generators of function fields
Martin Widmer
Let be a finite extension of a global field. Such an extension can be generated over by a single element. The aim of this article is to prove the existence of a "small" g…
Counting points of fixed degree and bounded height
Martin Widmer
We consider the set of points in projective -space that generate an extension of degree over given number field , and deduce an asymptotic formula for the number of such…
A note on generators of number fields
Jeffrey D. Vaaler, Martin Widmer
We establish upper bounds for the smallest height of a generator of a number field over the rational field $\Q$. Our first bound applies to all number fields having at leas…