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- W1965011238 abstract "Using the result of almost u.d. mod 1 and G. Hoheisel [6] and Emdös's result, Akiyama [1] gave a different proof of the Erdös and Turán result [4], i.e., Δ2 log pn changes its sign infinitely many times, where pn is the n-th prime number and Δ2 f(n) = Δ(Δf(n)), Δf(n) = f(n + 1)-f(n). In this paper, we show the neceasary condition for monotone almost uniform distribution mod 1. We give Fejér's type theorem for almost uniform distribution mod 1 and give a similar result of Niederreiter [8]. Also we obtain the converse of its result with some conditions. As an application, we give a simple proof [1] of Erdös and Turán's result using Erdös's result [cf. 3, 9, 10, 11, and 21. Also we obtain the condition of P(n) that Δ2 log P(n) changes its sign infinitely many times." @default.
- W1965011238 created "2016-06-24" @default.
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- W1965011238 date "1999-01-01" @default.
- W1965011238 modified "2023-09-25" @default.
- W1965011238 title "On Monotone Almost (P, μ) - u. d. Mod 1 Sequence" @default.
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- W1965011238 doi "https://doi.org/10.1002/mana.3212050102" @default.
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