3 citations · 4 across the 7 of their papers we have counts for
7 papers
Height lower bounds for elements of highly composite rings
Siu Hang Man, Niclas Technau, Martin Widmer +1
Let be the composite field of all number fields of degree at most . In 2001 Bombieri and Zannier proved that has the Northcott property and…
A short remark on the -torsion part of class groups
Martin Widmer
In a 2008 paper Ellenberg suggested a strategy to improve the known upper bounds for the -torsion part of class groups of number fields of fixed degree . Motivated by this…
Rational integers as sums of units -- the quadratic case
Christopher Frei, Martin Widmer, Volker Ziegler
How many natural numbers below can be written as a sum of units of the ring of integers of a given number field? We give the asymptotics as gets large for quadratic num…
Effective equidistribution of norm one elements in CM-fields
Shabnam Akhtari, Jeffrey D. Vaaler, Martin Widmer
For a number field let be the maximal subgroup of the multiplicative group that embeds into the unit circle under each embedding of into the comp…
Most totally real fields do not have universal forms or Northcott property
Nicolas Daans, Vitezslav Kala, Siu Hang Man +2
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…
Small generators of abelian number fields
Martin Widmer
We show that for each abelian number field of sufficiently large degree there exists an element with $K=\IQ(α)$ and absolute Weil height ,…
On the Northcott property for infinite extensions
Martin Widmer
We start with a brief survey on the Northcott property for subfields of the algebraic numbers $\Qbar$. Then we introduce a new criterion for its validity (refining the author's pre…