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11-XX Number theory
11Jxx Diophantine approximation, transcendental number theory
11J04 Homogeneous approximation to one number

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Displaying 61 – 80 of 84

Results on the ratios of the terms of second order linear recurrences

Péter Kiss (1991)

Mathematica Slovaca

Root separation for reducible integer polynomials

Yann Bugeaud, Andrej Dujella (2014)

Acta Arithmetica

We construct parametric families of (monic) reducible polynomials having two roots very close to each other.

Scharfe Irrationalitätsmaße für Zahlen, die mit Bessel-Funktionen zusammenhängen.

Peter Bundschuh (1979)

Mathematische Zeitschrift

Sets of exact approximation order by rational numbers III

Yann Bugeaud, Carlos Gustavo Moreira (2011)

Acta Arithmetica

Short proofs of theorems of Lekkerkerker and Ballieu.

Riederle, Max (1982)

International Journal of Mathematics and Mathematical Sciences

Simultaneous approximation to a real number and to its cube by rational numbers

Stéphane Lozier, Damien Roy (2012)

Acta Arithmetica

Suites colorées

Michel Waldschmidt (1975/1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Sur le spectre de Lagrange d'un ensemble de nombres réels

Michel Mendès France (1977/1978)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Symmetric and asymmetric Diophantine approximation of continued fractions

Jingcheng Tong (1989)

Bulletin de la Société Mathématique de France

The best Diophantine approximation functions by continued fractions

Jing Cheng Tong (1996)

Mathematica Bohemica

Let $ξ = [a_{0}; a_{1}, a_{2}, \dots, a_{i}, \dots]$ be an irrational number in simple continued fraction expansion, $p_{i} / q_{i} = [a_{0}; a_{1}, a_{2}, \dots, a_{i}]$ , $M_{i} = q_{i}^{2} | ξ - p_{i} / q_{i} |$ . In this note we find a function $G (R, r)$ such that $\begin{matrix} M_{n + 1} < R and M_{n - 1} < r imply M_{n} > G (R, r), & M_{n + 1} > R and M_{n - 1} > r imply M_{n} < G (R, r) . \end{matrix}$ Together with a result the author obtained, this shows that to find two best approximation functions $\tilde{H} (R, r)$ and $\tilde{L} (R, r)$ is a well-posed problem. This problem has not been solved yet.

The Conjugate Property of the Borel Theorem on Diophantine Approximation.

Jingcheng Tong (1983)

Mathematische Zeitschrift

The Lagrange spectrum of a set

T. Cusick, Michel Mendès France (1979)

Acta Arithmetica

The Rhin-Viola method for log 2

Raffaele Marcovecchio (2009)

Acta Arithmetica

Thue's Fundamentaltheorem, I: The general case

Paul M. Voutier (2010)

Acta Arithmetica

Transcendence measures of certain numbers whose transcendency was proved by A. Baker

P. L. Cijsouw (1974)

Compositio Mathematica

Transcendence measures of exponentials and logarithms of algebraic numbers

P. L. Cijsouw (1974)

Compositio Mathematica

Über Annäherungswerte algebraischer Zahlen.

Axel Thue (1909)

Journal für die reine und angewandte Mathematik

Über das Approximationsspektrum des Einheitskreises.

Hans Günther Kopetzky (1985)

Monatshefte für Mathematik

Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche.

A. Hurwitz (1891)

Mathematische Annalen

Une mesure de transcendance de $e^{π}$

Michel Waldschmidt (1975/1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Currently displaying 61 – 80 of 84

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