Simultaneous diophantine approximation in $\mathbb{R}^2 × \mathbb{C} × \mathbb{Q}_p$
Abstract
An analogue of the convergence part of Khintchine's
theorem (1924) for simultaneous approximation of integral
polynomials at the points
$(x_1,x_2,z,w)\in\mathbb{R}^2\times\mathbb{C}\times\mathbb{Q}_p$ is
proved. It is a solution of the more general problem than
Sprind\u{z}uk's problem (1980) in the ring of adeles. We use a new
form of the essential and nonessential domains method in metric
theory of Diophantine approximation.
theorem (1924) for simultaneous approximation of integral
polynomials at the points
$(x_1,x_2,z,w)\in\mathbb{R}^2\times\mathbb{C}\times\mathbb{Q}_p$ is
proved. It is a solution of the more general problem than
Sprind\u{z}uk's problem (1980) in the ring of adeles. We use a new
form of the essential and nonessential domains method in metric
theory of Diophantine approximation.
Full Text:
PDFDOI: https://doi.org/10.2478/tatra.v56i0.247