一类快速收敛有理数级数的无理性指数

IF 0.3 Q4 MATHEMATICS

Tsukuba Journal of Mathematics Pub Date : 2020-12-01 DOI:10.21099/TKBJM/20204402235

D. Duverney, T. Kurosawa, I. Shiokawa

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引用次数: 0

摘要

设{xn}是大于1的有理数序列，使得对于所有足够大的n，xn+1≥xn，并且设εn∈{−1，1}。在xn+1/x2n分母的一定增长条件下，我们证明了∑∞n=1εn/xn的非理性指数等于lim-supn→∞（log xn+1/log xn）。2010数学学科分类：11A55、11J70、11J82、11J91

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Irrationality exponents of certain fast converging series of rational numbers

Let {xn} be a sequence of rational numbers greater than one such that xn+1 ≥ xn for all sufficiently large n and let εn ∈ {−1, 1}. Under certain growth conditions on the denominators of xn+1/x 2 n we prove that the irrationality exponent of the number ∑∞ n=1 εn/xn is equal to lim supn→∞(log xn+1/ log xn). 2010 Mathematics Subject Classification: 11A55, 11J70, 11J82, 11J91

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Tsukuba Journal of Mathematics MATHEMATICS-

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14.30%

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