Geodesic
Diophantine Approximations of the Number~$\pi$ by Numbers from the Field $\mathbb Q(\sqrt{3})$
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 912-922

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We prove an estimate of the irrationality measure of any nonzero number of the form $r_1\pi+r_2\pi/\sqrt{3}$, $r_1,r_2\in\mathbb Q(\sqrt{3})$.
Mots-clés : Diophantine approximation
Keywords: the number $\pi$, the field $\mathbb Q(\sqrt{3})$, irrationality measure of a number, Kummer's formula, hypergeometric function, saddle-point method. 
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     author = {E. B. Tomashevskaya},
     title = {Diophantine {Approximations} of the {Number~}$\pi$ by {Numbers} from the {Field} $\mathbb Q(\sqrt{3})$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {912--922},
     publisher = {mathdoc},
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     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a9/}
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E. B. Tomashevskaya. Diophantine Approximations of the Number~$\pi$ by Numbers from the Field $\mathbb Q(\sqrt{3})$. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 912-922. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a9/