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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 3(381), Pages 163–164 (Mi umn9175)  

This article is cited in 17 scientific papers (total in 17 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

On the irrationality measure of $\pi$

V. Kh. Salikhov

Bryansk State Technical University

DOI: https://doi.org/10.4213/rm9175

Full text: PDF file (319 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2008, 63:3, 570–572

Bibliographic databases:

MSC: Primary 11J82; Secondary 11J25, 11J72, 33C60
Presented: А. В. Михалёв
Accepted: 24.01.2008

Citation: V. Kh. Salikhov, “On the irrationality measure of $\pi$”, Uspekhi Mat. Nauk, 63:3(381) (2008), 163–164; Russian Math. Surveys, 63:3 (2008), 570–572

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. V. Nesterenko, “On the Irrationality Exponent of the Number $\ln2$”, Math. Notes, 88:4 (2010), 530–543  mathnet  crossref  crossref  mathscinet  isi
    2. V. Kh. Salikhov, “On the Measure of Irrationality of the Number $\pi$”, Math. Notes, 88:4 (2010), 563–573  mathnet  crossref  crossref  mathscinet  isi
    3. Van Assche W., “Hermite-Padé rational approximation to irrational numbers”, Comput. Methods Funct. Theory, 10:2 (2010), 585–602  mathscinet  zmath  isi
    4. Laakkonen P., Pohjolainen S., “Directed structure at infinity for infinite-dimensional systems”, Internat. J. Control, 84:4 (2011), 702–715  crossref  mathscinet  zmath  isi  elib  scopus
    5. Laeng E., Pata V., “A convergence–divergence test for series of nonnegative terms”, Expo. Math., 29:4 (2011), 420–424  crossref  mathscinet  zmath  isi  elib  scopus
    6. Bashmakova M.G., “Dva podkhoda k otsenke mery irratsionalnosti znachenii gipergeometricheskoi funktsii s polutselymi parametrami”, Vestn. Bryanskogo gos. tekhnich. un-ta, 2011, no. 2, 114–120  elib
    7. Rivoal T., “On the convergence of Diophantine Dirichlet series”, Proc. Edinb. Math. Soc. (2), 55:2 (2012), 513–541  crossref  mathscinet  zmath  isi  scopus
    8. Kumchev A.V., “On the convergence of some alternating series”, Ramanujan J., 30:1 (2013), 101–116  crossref  mathscinet  zmath  isi  scopus
    9. W. Zudilin, “On the irrationality measure of $\pi^2$”, Russian Math. Surveys, 68:6 (2013), 1133–1135  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Guo Y.-J., Wen Zh.-X., Wu W., “On the Irrationality Exponent of the Regular Paperfolding Numbers”, Linear Alg. Appl., 446 (2014), 237–264  crossref  mathscinet  zmath  isi  scopus
    11. Leppala K., “Explicit lower bounds for linear forms”, Math. Comput., 85:302 (2016), 2995–3008  crossref  mathscinet  zmath  isi  scopus
    12. Steinerberger S., “Directional Poincaré inequalities along mixing flows”, Ark. Mat., 54:2 (2016), 555–569  crossref  mathscinet  zmath  isi  scopus
    13. M. G. Bashmakova, E. S. Zolotukhina, “O pokazatelyakh irratsionalnosti chisel vida $\sqrt{d}\ln{\frac{\sqrt{d}+1}{\sqrt{d}-1}}$”, Chebyshevskii sb., 18:1 (2017), 29–43  mathnet  crossref  elib
    14. V. G. Lysov, “O diofantovykh priblizheniyakh proizvedeniya logarifmov”, Preprinty IPM im. M. V. Keldysha, 2018, 158, 20 pp.  mathnet  crossref  elib
    15. Rzepnicki L., Schnaubelt R., “Polynomial Stability For a System of Coupled Strings”, Bull. London Math. Soc., 50:6 (2018), 1117–1136  crossref  mathscinet  zmath  isi  scopus
    16. 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
    17. V. Kh. Salikhov, M. G. Bashmakova, “O pokazatele irratsionalnosti $\mathrm{arctg}  \frac {1}{3}$”, Izv. vuzov. Matem., 2019, no. 1, 69–75  mathnet  crossref
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