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Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

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JournalAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze
DateAccepted/In press - 27 Mar 2019
DatePublished (current) - 22 Dec 2020
Issue numberSpecial 2020
Number of pages29
Pages (from-to)643-671
Original languageEnglish


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.

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