A new lower bound for (3/2) k
Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 311-323.

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 .

Received: 2005-07-08
Published online: 2008-12-03
DOI: https://doi.org/10.5802/jtnb.588
@article{JTNB_2007__19_1_311_0,
     author = {Wadim Zudilin},
     title = {A new lower bound for ${\Vert (3/2)^k\Vert }$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {19},
     number = {1},
     year = {2007},
     pages = {311-323},
     doi = {10.5802/jtnb.588},
     zbl = {1127.11049},
     mrnumber = {2332068},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2007__19_1_311_0/}
}
Zudilin, Wadim. A new lower bound for ${\Vert (3/2)^k\Vert }$. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 311-323. doi : 10.5802/jtnb.588. https://jtnb.centre-mersenne.org/item/JTNB_2007__19_1_311_0/

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