An effective lower bound for the height of algebraic numbers

From MaRDI portal
Publication:4855033

DOI10.4064/aa-74-1-81-95zbMath0838.11065arXiv1211.3110OpenAlexW1493538398MaRDI QIDQ4855033

Paul M. Voutier

Publication date: 7 January 1996

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3110




Related Items

Arithmetic groups and the Lehmer conjectureUnnamed ItemPisot unit generators in number fieldsAlgebraic Number StarscapesUniform explicit Stewart theorem on prime factors of linear recurrencesRemarks on Euclidean minimaA relationship between the Mahler measure and the discriminant of algebraic numbersProperties of trinomials of height at least \(2\)Lehmer's problem on \(\mathbb G_m\) and the method of slopesContinued fraction expansions in connection with the metric Mahler measureThe Catalan equationFactoring bivariate sparse (lacunary) polynomialsOn the multiplicative independence of the roots of generalized Fibonacci and Pell polynomialsThe Korteweg-de Vries equation and a Diophantine problem related to Bernoulli polynomialsOn divisors of Lucas and Lehmer numbers\(p\)-adic logarithmic forms and a problem of ErdősSingular intersections of subgroups and character varietiesShimura curves and the abc conjectureThe Schanuel theorem in adelic Hermitian bundlesLower bounds for regulators of number fields in terms of their discriminantsMetric Mahler measures over number fieldsCounting exceptional points for rational numbers associated to the Fibonacci sequenceThe distance to square-free polynomialsThe arithmetic and geometry of Salem numbersHolomorphic functions on bundles over annuliRepresentation of unity by binary formsRationality of exponential functions at integer argumentsQuantum automata and algebraic groupsPrimitive divisors of Lucas and Lehmer sequences. IIExplicit small heights in infinite non-abelian extensionsSome consequences of Masser's counting theorem on elliptic curvesOn the metric Mahler measureCovolumes, units, regulator: conjectures by D. Bertrand and F. Rodriguez-VillegasPerfect powers in the summatory function of the power towerInteger transfinite diameter and polynomials with small Mahler measurePolynomial interpolation on an order of a number fieldEffective bounds for solutions of \(S\)-unit equations and of Thue-Mahler equationsSmall generators of cocompact arithmetic Fuchsian groupsAlmost powers in the Lucas sequenceOn the distribution of roots of polynomials in sectors. IOn the distribution of roots of polynomials in sectors. IIQuantitative height bounds under splitting conditionsBinary polynomial power sums vanishing at roots of unityA polynomial time test to detect numbers with many exceptional pointsThe mean values of logarithms of algebraic integersOn the zeros of the derivatives of certain polynomialsOn the smallest value of the maximal modulus of an algebraic integerOn the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp formsThe zero multiplicity of linear recurrence sequencesIntervals without primes near elements of linear recurrence sequencesUniversal systole bounds for arithmetic locally symmetric spaces