Geodesic
On the Irrationality Measures of Certain Numbers.~II
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 582-591.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the irrationality measures of the numbers $\sqrt{2k-1}\,\operatorname{arctan}(\sqrt{2k-1}/(k-1))$, where $k$ is an even positive integer, upper bounds are presented.
Keywords: irrationality measure. 
@article{MZM_2018_103_4_a9,
     author = {A. A. Poljanskij},
     title = {On the {Irrationality} {Measures} of {Certain} {Numbers.~II}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {582--591},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a9/}
}
TY  - JOUR
AU  - A. A. Poljanskij
TI  - On the Irrationality Measures of Certain Numbers.~II
JO  - Matematičeskie zametki
PY  - 2018
SP  - 582
EP  - 591
VL  - 103
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a9/
LA  - ru
ID  - MZM_2018_103_4_a9
ER  - 
%0 Journal Article
%A A. A. Poljanskij
%T On the Irrationality Measures of Certain Numbers.~II
%J Matematičeskie zametki
%D 2018
%P 582-591
%V 103
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a9/
%G ru
%F MZM_2018_103_4_a9
A. A. Poljanskij. On the Irrationality Measures of Certain Numbers.~II. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 582-591. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a9/

[1] M. Hata, “Rational approximations to $\pi$ and some other numbers”, Acta Arith., 63:4 (1993), 335–349 | DOI | MR | Zbl

[2] V. A. Androsenko, V. Kh. Salikhov, “Integral Markovekkio i mera irratsionalnosti $\frac{\pi}{\sqrt{3}}$”, Vestn. BGTU, 34:4 (2011), 129–132

[3] R. Marcovecchio, “The Rhin–Viola method for $\log 2$”, Acta Arith., 139:2 (2009), 147–184 | DOI | MR | Zbl

[4] V. A. Androsenko, “Mera irratsionalnosti chisla $\frac{\pi}{\sqrt{3}}$”, Izv. RAN. Ser. matem., 79:1 (2015), 3–20 | DOI | MR | Zbl

[5] Yu. V. Nesterenko, “O pokazatele irratsionalnosti chisla $\ln2$”, Matem. zametki, 88:4 (2010), 549–564 | DOI | MR | Zbl

[6] M. G. Bashmakova, “Estimates for the exponent of irrationality for certain values of hypergeometric functions”, Mosc. J. Comb. Number Theory, 1:1 (2011), 67–78 | MR | Zbl

[7] A. A. Polyanskii, “O kvadratichnom pokazatele irratsionalnosti $\ln 2$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 1, 23–28 | MR | Zbl

[8] A. A. Polyanskii, “On the irrationality measure of certain numbers”, Mosc. J. Comb. Number Theory, 1:4 (2011), 80–90 | MR | Zbl

[9] A. A. Polyanskii, “O kvadratichnykh pokazatelyakh irratsionalnosti nekotorykh chisel”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2013, no. 5, 25–29 | MR | Zbl

[10] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza. Ch. 2. Transtsendentnye funktsii, Fizmatgiz, M., 1963 | Zbl

[11] A. A. Polyanskii, O pokazatelyakh irratsionalnosti nekotorykh chisel, Dis. $\dots$ kand. fiz.-matem. nauk, MGU, 2013 http://polyanskii.com/wp-content/uploads/thesis/polyanskii-phd.pdf

[12] M. Hata, “$\mathbb{C}^2$-saddle method and Beuker's integral”, Trans. Amer. Math. Soc., 352:10 (2000), 4557–4583 | DOI | MR | Zbl