Simultaneous Diophantine approximation in $\mathbb{R}²×\mathbb{C}×\mathbb{Q}_p$

Rok, strany: 2013, 79 - 86

An analogue of the convergence part of Khintchine's theorem (1924) for simultaneous approximation of integral polynomials at the points

$$ (x₁,x₂,z,w)\in\mathbb{R}²×\mathbb{C}×\mathbb{Q}_p $$

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 domain methods in metric theory of Diophantine approximation.

ISO 690:

Kovalevskaya, E. 2013. Simultaneous Diophantine approximation in $\mathbb{R}²×\mathbb{C}×\mathbb{Q}_p$. In Tatra Mountains Mathematical Publications, vol. 56, no.3, pp. 79-86. 1210-3195.

APA:

Kovalevskaya, E. (2013). Simultaneous Diophantine approximation in $\mathbb{R}²×\mathbb{C}×\mathbb{Q}_p$. Tatra Mountains Mathematical Publications, 56(3), 79-86. 1210-3195.