Geodesic
On irrationality measure $\mathrm{arctg}\, \frac {1}{3}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 69-75

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We investigate the arithmetic properties of the value $\mathrm{arctg}\, \frac {1}{3}$. We elaborate special integral construction with the property of symmetry for evaluating irrationality measure of this number. We research linear form, generated by this integral, and prove a new result for extent of the irrationality of $\mathrm{arctg}\, \frac {1}{3}$, which improves the previous one.
Keywords: irrationality measure, linear form. 
@article{IVM_2019_1_a6,
     author = {V. Kh. Salikhov and M. G. Bashmakova},
     title = {On irrationality measure $\mathrm{arctg}\, \frac {1}{3}$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {69--75},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_1_a6/}
}
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V. Kh. Salikhov; M. G. Bashmakova. On irrationality measure $\mathrm{arctg}\, \frac {1}{3}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 69-75. http://geodesic.mathdoc.fr/item/IVM_2019_1_a6/