Khintchine's theorem and transference principle for star bodies
by M. M. Dodson and S. Kristensen
Preprints
Number 2 (January 2006)
Analogues of Khintchine's Theorem in simultaneous Diophantine approximation in the plane are proved with the classical height replaced by fairly general planar distance functions or equivalently star bodies. Khintchine's transference principle is discussed for distance functions and a direct proof for the multiplicative version is given. A transference principle is also established for a different distance function.
Published in Int. J. Number Theory 2(3) (2006), pp. 431-453.