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Around the Littlewood conjecture in Diophantine approximation

Yann Bugeaud (2014)

Publications mathématiques de Besançon

The Littlewood conjecture in Diophantine approximation claims that $inf_{q \geq 1} q \cdot ∥ q α ∥ \cdot ∥ q β ∥ = 0$ holds for all real numbers $α$ and $β$ , where $∥ \cdot ∥$ denotes the distance to the nearest integer. Its $p$ -adic analogue, formulated by de Mathan and Teulié in 2004, asserts that $inf_{q \geq 1} q \cdot ∥ q α ∥ \cdot {| q |}_{p} = 0$ holds for every real number $α$ and every prime number $p$ , where ${| \cdot |}_{p}$ denotes the $p$ -adic absolute value normalized by ${| p |}_{p} = p^{- 1}$ . We survey the known results on these conjectures and highlight recent developments.

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Displaying 21 – 40 of 84

Around the Littlewood conjecture in Diophantine approximation

Bemerkungen zu einem Approximationssatz für regelmäßige Kettenbrüche.

Best diophantine approximations for ternary linear forms.

Billiards and the five distance theorem

Characteristic approximation properties of quadratic irrationals.

Diophantine approximation by square-free numbers

Diophantine approximation in short intervals

Diphantine Approximation with Square-free Numbers.

Distribution of closed geodesics on the modular surface and quadratic irrationals

Dyson's Lemma for polynomials in several variables (and the Theorem of Roth).

Eine Bemerkung über diophantische Approximationen von ea, a ...0 rational.

Explicit lower bounds for ${| | (3 / 2)}^{k} | |$

Irrationality measures of $log 2$ and $π / \sqrt{3}$ .

La «nouvelle technique» de Hooley

Limit points in the Lagrange spectrum of a quadratic field

Linear forms in two logarithms and Schneider's method (III)

Mahler's classification of numbers compared with Koksma's

Mesures d'irrationalité de log 2.

Metric Diophantine approximation with two restricted variables. IV. Miscellaneous results

Old Friends Revisited; the Multifunctional Nature of Some Classical Functions.

Currently displaying 21 – 40 of 84