A Lower Bound for the Height in Abelian Extensions

By F. Amoroso, R. Dvornicich. 2000

127 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/aa82b05f258e471c425552af9e890e7bf895ca6e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. P. Habegger

In Geometry and Topology

1. Michael J. Mossinghoff
2. P. Habegger

In Theoretical Computer Science

1. P. Habegger

Citations in the corpus

• Small height and infinite nonabelian extensions (2011, background): “A dichotomy into an unramified and a ramified case already appeared in the original work of Amoroso-Dvornicich on abelian extensions of Q.”
• Lehmer's problem for polynomials with odd coefficients (2007, background): “In addition, Amoroso and Dvornicich [1] showed that if f is an irreducible, noncyclotomic polynomial of degree d whose splitting field is an abelian extension of Q, then M(f) ≥ 5d/12.”
• Number Theory and Polynomials: The Mahler measure of algebraic numbers: a survey (2007, unknown): “Amoroso and Dvornicich [10, p. 261] gave the interesting example of α = 1 2 √ 3 + √ −7, not an algebraic integer, where |α| = 1, Q(α) is Kroneckerian, but M(α) = 2 φ2.”