Metric Considerations Concerning the Mixed Littlewood Conjecture

TY - JOUR

T1 - Metric Considerations Concerning the Mixed Littlewood Conjecture

AU - Haynes, A

AU - Velani, Sanju

AU - Bugeaud, Yann

PY - 2011/5

Y1 - 2011/5

N2 - The main goal of this paper 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.

AB - The main goal of this paper 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.

KW - Number Theory

U2 - 10.1142/S1793042111004289

DO - 10.1142/S1793042111004289

M3 - Article

SN - 1793-0421

VL - 7

SP - 593

EP - 609

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 3

ER -