The convergence part of a Knintchine-type theorem in the ring of adeles

Rok, strany: 2014, 39 - 50

We prove the convergence part of a Khintchine-type theorem for simultaneous Diophantine approximation of zero by values of integral polynomials at the points

$$ (x,z,ω₁,ω₂)\in \mathbb{R}×\mathbb{C}×\mathbb{Q}_p1×\mathbb{Q}_p2, $$

where $p₁\neq p₂$ are primes. It is a generalization of Sprind\u{z}uk's problem (1980) in the ring of adeles. We continue our investigation (2013), where the problem was proved at the points in $\mathbb{R}²×\mathbb{C}×\mathbb{Q}_p1$. We use the most precise form of the essential and inessential domains method in metric theory of Diophantine approximation.

ISO 690:

Kovalevskaya, E. 2014. The convergence part of a Knintchine-type theorem in the ring of adeles. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 39-50. 1210-3195.

APA:

Kovalevskaya, E. (2014). The convergence part of a Knintchine-type theorem in the ring of adeles. Tatra Mountains Mathematical Publications, 59(2), 39-50. 1210-3195.