Metric considerations concerning the mixed Littlewood Conjecture

Details Metric considerations concerning the mixed Littlewood Conjecture Metric considerations concerning the mixed Littlewood Conjecture

2009-09-22

arxiv.org/abs/0909.3923v2

Mathematics

Number Theory

17 pages, corrected various oversights.

Scientific paper

The main goal of this note is to develop a metrical theory of Diophantine
approximation within the framework of the de Mathan-Teulie Conjecture, also
known as the `Mixed Littlewood Conjecture'. Let p be a prime. A consequence of
our main result is that, for almost every real number \alpha,
\liminf_{n\rar\infty}n(\log n)^2|n|_p\|n\alpha\|=0.

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