An effective lower bound for the height of algebraic numbers
By P. Voutier. 2012
157 citations recorded by the source corpus.
We prove that if $\alpha$ is a non-zero algebraic number of degree $d \geq 2$ which is not a root of unity, then $dh(\alpha)>(1/4) (\log(\log (d))/\log(d))^3.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2bbc3f62a6b62a04db60cd102d96080d90638605
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In Algebra and Number Theory
In Computational Theory and Mathematics
- Samir Siksek
- Yann Bugeaud
- Maurice Mignotte
- Szabolcs Tengely
- Michael Stoll
- Manjul Bhargava
- Nuno Freitas
- Bao V. Le Hung
In Geometry and Topology
- Samir Siksek
- Maurice Mignotte
- Yann Bugeaud
- Szabolcs Tengely
- Michael Stoll
- Manjul Bhargava
- Nuno Freitas
- Bao V. Le Hung
Citations in the corpus
- Integral points on hyperelliptic curves (2008, background): “We need the following result of Voutier [51] concerning Lehmer’s problem.”
- Bounds for the solutions of S-unit equations and decomposable form equations (2005, unknown): “To prove (iii), it is enough to combine the proof of (iii) in Lemma 1 of [5] with the inequality (19) dh(εi) ≥ { log 2 if d = 1, 2/(log 3d)3 if d ≥ 2, which, for d ≥ 2, is due to Voutier [30].”
- The arithmetic and geometry of Salem numbers (2001, unknown): “In any case, a sample of such a result is the Theorem 24 (Voutier, [51]) If P (X) is not a cyclotomic polynomial, and has degree d > 1, then”
- Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers (2004, background): “Bilu, G. Hanrot and P. M. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers.”