Metric discrepancy results for geometric progressions with small ratios
Metric discrepancy results for geometric progressions with small ratios
复制标题
小比率几何级数的公制差异结果
DOI：
10.1007/s10474-018-0805-z
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发表时间：
2018
影响因子：
0.9
通讯作者：
Tscheckl M.
中科院分区：
文献类型：
--
作者：
Fukuyama K.;Sakaguchi S.;Shimabe O.;Toyoda T.;Tscheckl M.
虽然证明了几何级数的偏差的重对数律，但对于小比例，出现在那里的常数并没有得到具体的估计。我们考虑了该比率是一个小有理数的幂的情况，并对该常数的具体值作了一个猜想。我们给出了几个与猜想相符的例子。
Although the law of the iterated logarithm for discrepancies of geometric progression is proved, the constants appearing there are not concretely evaluated for small ratios. We consider the case when the ratio is a power root of a small rational number, and make a conjecture on the concrete value of the constant. We give several examples which are consistent with the conjecture.