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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 1, Pages 3–20 (Mi izv8259)  

This article is cited in 6 scientific papers (total in 6 papers)

Irrationality measure of the number $\frac{\pi}{\sqrt{3}}$

V. A. Androsenko

Bryansk State Technical University

Abstract: Using a new integral construction combining the idea of symmetry suggested by Salikhov in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for the irrationality measure of $\frac{\pi}{\sqrt{3}}$.

Keywords: irrationality measure, linear form, complex integral.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00171
The research was partially financially supported by the RFBR (grant no. 12-01-00171).


DOI: https://doi.org/10.4213/im8259

Full text: PDF file (553 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:1, 1–17

Bibliographic databases:

UDC: 511.36
MSC: 11J82
Received: 05.06.2014

Citation: V. A. Androsenko, “Irrationality measure of the number $\frac{\pi}{\sqrt{3}}$”, Izv. RAN. Ser. Mat., 79:1 (2015), 3–20; Izv. Math., 79:1 (2015), 1–17

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Yu. Luchin, V. Kh. Salikhov, “Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2} )$”, Izv. Math., 82:3 (2018), 549–577  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. A. Poljanskij, “On the Irrationality Measures of Certain Numbers. II”, Math. Notes, 103:4 (2018), 626–634  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. G. Bashmakova, E. S. Zolotukhina, “Ob otsenke mery irratsionalnosti chisel vida $\sqrt{4k+3}\ln{\frac{\sqrt{4k+3}+1}{\sqrt{4k+3}-1}}$ i $\frac{1}{\sqrt{k}}\mathrm{arctg} {\frac{1}{\sqrt{k}}}$”, Chebyshevskii sb., 19:2 (2018), 15–29  mathnet  crossref  elib
    4. A. A. Polyanskii, “On simultaneous approximations of $\ln3$ and $\pi/\sqrt3$ by rational numbers”, Sb. Math., 210:4 (2019), 589–605  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. M. G. Bashmakova, V. Kh. Salikhov, “Ob otsenke mery irratsionalnosti $\mathop{\mathrm{arctg}}\frac12$”, Chebyshevskii sb., 20:4 (2019), 58–68  mathnet  crossref
    6. A. V. Begunts, “On the Convergence of Alternating Series Associated with Beatty Sequences”, Math. Notes, 107:2 (2020), 345–349  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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