Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1

From MaRDI portal
Publication:2720955

DOI10.1515/crll.2001.044zbMath1002.11059OpenAlexW2061418840MaRDI QIDQ2720955

Michael A. Bennett

Publication date: 28 June 2001

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2001.044




Related Items (33)

On a cubic family of Thue equations involving Fibonacci numbers and powers of twoPowers in recurrence sequences: Pell equationsOdd values of the Ramanujan tau functionAn explicit density estimate for Dirichlet $L$-seriesEXPLICIT ZERO‐FREE REGIONS FOR DIRICHLET ‐FUNCTIONSTWIN SQUAREFUL NUMBERSThe Diophantine equation \((ax^k-1)(by^k-1)=abz^k-1\)A UNIQUE PERFECT POWER DECAGONAL NUMBERImproved constants for effective irrationality measures from hypergeometric functionsNew bounds and conditions for the equation of Nagell-LjunggrenStarting with gaps between k-free numbersDiagonalizable Thue equations: revisitedEffective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equationsThe number of solutions to the trinomial Thue equationOn equation Xn − 1 = BZnExplicit Estimates: From Λ(n) in Arithmetic Progressions to Λ(n)/nPower savings for counting solutions to polynomial-factorial equationsOn the representation of unity by binary cubic formsUnnamed ItemOn unit power integral bases of \(\mathbb Z[\root 4 \of {m}\)] ⋮ The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\)Thue's inequalities and the hypergeometric methodThe generalized Pillai equation \(\pm ra^x\pm sb^y=c\)ON THE SQUARE-FREE PARTS OF ⌊en!⌋Mahler and transcendence: effective constructions in transcendental number theoryOn the power values of power sumsRepresentation of integers by sparse binary formsThue's equation as a tool to solve two different problemsThe Generalized Nagell–Ljunggren Problem: Powers with Repetitive RepresentationsOn the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\).The Nagell-Ljunggren equation via Runge's methodPadé approximation for a class of hypergeometric functions and parametric geometry of numbersLinear Forms in Logarithms



Cites Work


This page was built for publication: Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1