An analogue of the convergence part of Khintchine'stheorem (1924) for simultaneous approximation of integralpolynomials at the points$(x_1,x_2,z,w)\in\mathbb{R}^2\times\mathbb{C}\times\mathbb{Q}_p$ isproved. It is a solution of the more general problem thanSprind\u{z}uk's problem (1980) in the ring of adeles. We use a newform of the essential and nonessential domains method in metrictheory of Diophantine approximation.
@article{247,
title = {Simultaneous diophantine approximation in $\mathbb{R}^2 $\times$ \mathbb{C} $\times$ \mathbb{Q}\_p$},
journal = {Tatra Mountains Mathematical Publications},
volume = {55},
year = {2013},
doi = {10.2478/tatra.v56i0.247},
language = {EN},
url = {http://dml.mathdoc.fr/item/247}
}
Kovalevskaya, Ella. Simultaneous diophantine approximation in $\mathbb{R}^2 × \mathbb{C} × \mathbb{Q}_p$. Tatra Mountains Mathematical Publications, Tome 55 (2013) . doi : 10.2478/tatra.v56i0.247. http://gdmltest.u-ga.fr/item/247/