|
This article is cited in 1 scientific paper (total in 1 paper)
Estimates of the Averaged Sums of Fractional Parts
E. A. Sevast'yanov, I. Yu. Yakupov National Engineering Physics Institute "MEPhI", Moscow
Abstract:
We establish asymptotically sharp estimates for the sums of the inverses (and more general sums) of the fractional parts $\{i\theta\}$ of irrational numbers $\theta$, depending on the arithmetical characteristics of the numbers $\theta$.
Keywords:
averaged sum of fractional parts, irrational number, continued fraction, convergent, monotone function, Abel transformation, Khinchin's theorem.
Received: 08.04.2015 Revised: 25.04.2015
Citation:
E. A. Sevast'yanov, I. Yu. Yakupov, “Estimates of the Averaged Sums of Fractional Parts”, Mat. Zametki, 99:2 (2016), 298–308; Math. Notes, 99:2 (2016), 320–329
Linking options:
https://www.mathnet.ru/eng/mzm10677https://doi.org/10.4213/mzm10677 https://www.mathnet.ru/eng/mzm/v99/i2/p298
|
Statistics & downloads: |
Abstract page: | 361 | Full-text PDF : | 83 | References: | 58 | First page: | 31 |
|