Metric Diophantine Approximation : aspects of recent work

By Victor Beresnevich, Felipe A. Ram'irez, Sanju Velani. 2016

93 citations recorded by the source corpus.

In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarnik, Duffin-Schaeffer and Gallagher. We then describe recent strengthening of various classical statements as well as recent developments in the area of Diophantine approximation on manifolds. The latter includes the well approximable, the badly approximable and the inhomogeneous aspects.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0ab7fb9c1bc3f39d0810fe1b3eeee37cd599d9f0