Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

Abstract

We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on manifolds and to weighted badly approximable vectors. Finally, we interpret and prove a conjecture of Beresnevich-Velani (2010) about inhomogeneous intermediate exponents.

arXiv commentMinor revisions following referee report. This is the final version. To appear in Annali Della Scuola Normale Superiore Di Pisa

References in corpus (1)

• On Diophantine exponents and Khintchine's transference principle

Cited by in corpus (1)

• A geometric proof of Jarnik's identity in the setting of weighted simultaneous approximation