Metric Diophantine Approximation: aspects of recent work

TY - CHAP

T1 - Metric Diophantine Approximation

T2 - aspects of recent work

AU - Beresnevich, Victor

AU - Ramirez, Felipe Alberto

AU - Velani, Sanju

N1 - © Cambridge University Press/the authors, 2017. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2017/1

Y1 - 2017/1

N2 - 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.

AB - 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.

M3 - Chapter (peer-reviewed)

SN - 9781107552371

T3 - London Mathematical Society Lecture Note Series

SP - 1

EP - 95

BT - Dynamics and Analytic Number Theory

A2 - Badziahin, D.

A2 - Gorodnik, A.

A2 - Peyerimhoff, N.

PB - Cambridge University Press

ER -