Metric discrepancy results for geometric progressions with small ratios

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Metric discrepancy results for geometric progressions with small ratios

Fukuyama, K.; Sakaguchi, S.; Shimabe, O.; Toyoda, T.; Tscheckl, M.

Acta mathematica Hungarica, 08/2018, Volume: 155, Issue: 2

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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.

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Fukuyama, K. | Sakaguchi, S. | Shimabe, O. | Toyoda, T. | Tscheckl, M.

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