Khintchine's theorem and transference principle for star bodies

Details Khintchine's theorem and transference principle for star bodies Khintchine's theorem and transference principle for star bodies

2006-01-12

arxiv.org/abs/math/0601286v1

Mathematics

Number Theory

3 figures

Scientific paper

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.

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