42 citations · 105 across the 14 of their papers we have counts for
18 papers
Small integral generators of totally complex number fields
Shabnam Akhtari, Jeffrey Vaaler, Martin Widmer
Let be an algebraic number field and the absolute Weil height. Write for a certain positive constant that is an invariant of . We consider the question: does c…
Lower Bounds for Regulators of Number Fields in terms of their Discriminants
Shabnam Akhtari, Jeffrey D. Vaaler
We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such general inequalities…
A bound for the exterior product of -units
Shabnam Akhtari, Jeffrey D. Vaaler
We generalize an inequality for the determinant of a real matrix proved by A. Schinzel, to more general exterior products of vectors in Euclidean space. We apply this inequality to…
Lower bounds for Mahler measure that depend on the number of monomials
Shabnam Akhtari, Jeffrey D. Vaaler
We prove a new lower bound for the Mahler measure of a polynomial in one and in several variables that depends on the complex coefficients, and the number of monomials. In one vari…
Multiplicative approximation by the Weil height
Robert Grizzard, Jeffrey D. Vaaler
Let be an algebraic extension of fields, and let be contained in an algebraic closure of . If can be approximated by roots of numbers in $K^{\times…
On the height of solutions to norm form equations
Shabnam Akhtari, Jeffrey D. Vaaler
Let be a number field. We consider norm form equations associated to a full -module contained in a finite extension field . It is known that the set of solutions is nat…