Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583395 | Finite Fields and Their Applications | 2007 | 11 Pages |
Abstract
In a recent paper, the first and third author proved a central limit theorem for the number of coprime solutions of the Diophantine approximation problem for formal Laurent series in the setting of the classical theorem of Khintchine. In this note, we consider a more general setting and show that even an invariance principle holds, thereby improving upon earlier work of the second author. Our result yields two consequences: (i) the functional central limit theorem and (ii) the functional law of the iterated logarithm. The latter is a refinement of Khintchine's theorem for formal Laurent series. Despite a lot of research efforts, the corresponding results for Diophantine approximation of real numbers have not been established yet.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory