A new lower bound for ${\Vert (3/2)^k\Vert }$

Wadim Zudilin

doi:10.5802/jtnb.588

A new lower bound for

{∥ (3 / 2)}^{k} ∥

Wadim Zudilin ¹

¹ Department of Mechanics and Mathematics Moscow Lomonosov State University Vorobiovy Gory, GSP-2 119992 Moscow, Russia

Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 1, pp. 311-323.

Abstract (VO)
Résumé

We prove that, for all integers $k$ exceeding some effectively computable number $K$ , the distance from ${(3 / 2)}^{k}$ to the nearest integer is greater than $0 . 5803^{k}$ .

Nous démontrons que pour tout entier $k$ supérieur à une constante $K$ effectivement calculable, la distance de ${(3 / 2)}^{k}$ à l’entier le plus proche est minorée par $0, 5803^{k}$ .

MR Zbl

DOI : 10.5802/jtnb.588

Affiliations des auteurs :

Wadim Zudilin ¹

¹ Department of Mechanics and Mathematics Moscow Lomonosov State University Vorobiovy Gory, GSP-2 119992 Moscow, Russia

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Wadim Zudilin. A new lower bound for ${\Vert (3/2)^k\Vert }$. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 1, pp. 311-323. doi : 10.5802/jtnb.588. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.588/

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Cité par 8 documents. Sources : Crossref, zbMATH