Hajime Kaneko

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Let α > 1 be an algebraic number and ξ a nonzero real number. In this paper, we compute the range of the fractional parts {ξα n } (n = 0, 1,. . .). In particular, we estimate the maximal and minimal limit points. Our results show, for example, that if θ(= 24.97. . .) is the unique zero of the polynomial 2X 2 − 50X + 1 with X > 1, then there exists a nonzero(More)
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