On a mixed Khintchine problem in Diophantine approximation

Details On a mixed Khintchine problem in Diophantine approximation On a mixed Khintchine problem in Diophantine approximation

2012-01-23

arxiv.org/abs/1201.4694v1

Mathematics

Number Theory

16 pages

Scientific paper

We establish a `mixed' version of a fundamental theorem of Khintchine within the field of simultaneous Diophantine approximation. Via the notion of ubiquity we are able to make significant progress towards the completion of the metric theory associated with mixed problems in this setting. This includes finding a natural mixed analogue of the classical Jarn\'ik-Besicovich Theorem. Previous knowledge surrounding mixed problems was almost completely restricted to the multiplicative setup of de Mathan & Teuli\'e [21], where the concept originated.

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