Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
From MaRDI portal
Publication:1352648
DOI10.1006/jnth.1996.0152zbMath0870.11045OpenAlexW2036649879MaRDI QIDQ1352648
Publication date: 11 September 1997
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1996.0152
Taylor expansionsapproximation of zerosinterpolation determinant\(p\)-adic analog for lower bounds on the absolute value of integral linear combinations of logarithmsSchneider transcendence methodspecial values of Schur polynomials
Linear forms in logarithms; Baker's method (11J86) Approximation in non-Archimedean valuations (11J61)
Related Items
On integers with identical digits ⋮ Exponential Diophantine Equations ⋮ Differences between perfect powers: The Lebesgue-Nagell equation ⋮ On a mixed Littlewood conjecture for quadratic numbers ⋮ On a variant of Pillai's problem involving \(S\)-units and Fibonacci numbers ⋮ On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\) ⋮ On divisors of Lucas and Lehmer numbers ⋮ Logarithms of algebraic numbers ⋮ The Diophantine equations \(P_n^x+P_{n+1}^y=P_m^x\) or \(P_n^y+P_{n+1}^x=P_m^x\) ⋮ On the solutions of the Diophantine equation \(P_n \pm \frac{a(10^m -1)}{9}=k!\) ⋮ SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n! ⋮ On a variant of Pillai’s problem with binary recurrences and S-units ⋮ Effective resolution of Diophantine equations of the form \(u_n+u_m=w p_1^{z_1} \dotsm p_s^{z_s}\) ⋮ On the existence of S-Diophantine quadruples ⋮ Differences between perfect powers: prime power gaps ⋮ Effective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equations ⋮ On the Diophantine equation \(2^x=x^2+y^2-2\) ⋮ On the Diophantine equation \(x^2 - 4p^m = \pm y^n\) ⋮ On a conjecture of Erdős and Stewart ⋮ Factoriangular numbers in balancing and Lucas-balancing sequence ⋮ Lucas factoriangular numbers ⋮ Finding all \(S\)-Diophantine quadruples for a fixed set of primes \(S\) ⋮ On the diophantine equation $x^2-2^m=\pm y^n$ ⋮ On the equation \(y^x\pm x^y=z^2\) ⋮ Fibonacci factoriangular numbers ⋮ On simple \(K_4\)-groups ⋮ A note on the paper by Bugeaud and Laurent ``Minoration effective de la distance \(p\)-adique entre puissances de nombres algébriques ⋮ Perfect powers in the summatory function of the power tower ⋮ Effective bounds for solutions of \(S\)-unit equations and of Thue-Mahler equations ⋮ Difference between powers and squares of integers ⋮ Pell factoriangular numbers ⋮ A note on divisible points of curves ⋮ On binomial Thue-Mahler equations ⋮ Sums of factorials in binary recurrence sequences ⋮ Binomial coefficients and Lucas sequences ⋮ Divisibility properties of binary recurrent sequences ⋮ On the convergence of series of reciprocals of primes related to the Fermat numbers ⋮ On a Diophantine equation involving Fibonacci numbers and the Ramanujan \(\tau\)-function of factorials
