Diophantine approximation on curves and the distribution of rational points: Contributions to the divergence theory

V. Beresnevich, R. C. Vaughan, S. Velani, E. Zorin

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we develop an explicit method for studying the distribution of rational points near manifolds. As a consequence we obtain optimal lower bounds on the number of rational points of bounded height lying at a given distance from an arbitrary non-degenerate curve in Rn. This generalises previous results for analytic non-degenerate curves. Furthermore, the main results are proved in the inhomogeneous setting. For n≥3, the inhomogeneous aspect is new even under the additional assumption of analyticity. Applications of the main distribution theorem also include the inhomogeneous Khintchine-Jarník type theorem for divergence for arbitrary non-degenerate curves in Rn.

Original languageEnglish (US)
Article number107861
JournalAdvances in Mathematics
Volume388
DOIs
StatePublished - Sep 17 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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