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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 736–747 (Mi mz8516)  

Rational Approximations of the Number $\sqrt[3]{3}$

Yu. A. Pupyrev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain estimates of the form $\|\xi\alpha^n\|>C^k$ for all $k\ge K$ for the values $\xi=3^{1/3}$ and $\alpha=2$, where $K$ is an effective constant and $\|\cdot\|$ denotes the distance to the nearest integer.

Keywords: Padé approximant, Pfaff–Saalschütz summation formula, Cauchy's theorem, Laplace method, effective estimate, Laplace method, gamma function

DOI: https://doi.org/10.4213/mzm8516

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English version:
Mathematical Notes, 2009, 86:5, 693–703

Bibliographic databases:

UDC: 511.3
Received: 12.02.2009

Citation: Yu. A. Pupyrev, “Rational Approximations of the Number $\sqrt[3]{3}$”, Mat. Zametki, 86:5 (2009), 736–747; Math. Notes, 86:5 (2009), 693–703

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