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(1)

Journal de Th´

eorie des Nombres

de Bordeaux

19

(2007), 311–323

A new lower bound for

k

(3

/

2)

k

k

par

Wadim ZUDILIN

R´esum´e. Nous d´emontrons que pour tout entier k sup´erieur `a

une constanteKeffectivement calculable, la distance de (3/2)k

` a l’entier le plus proche est minor´ee par 0,5803k

.

Abstract. We prove that, for all integersk exceeding some

ef-fectively computable numberK, the distance from (3/2)k

to the nearest integer is greater than 0.5803k

.

WadimZudilin

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

119992 Moscow, Russia

URL:http://wain.mi.ras.ru/

E-mail:[email protected]

Referensi

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