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Counting rational approximations on rank one flag varieties

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arxiv 2410.16508 v1 pith:2YBPOQZN submitted 2024-10-21 math.NT math.DS

René Pfitscher This is my paper · ORCID
classification math.NTmath.DS
keywords approximationsflagrankrationalvarietiesaccordingapplychosen
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On a generalized flag variety of rank one, we count rational approximations to a real point chosen randomly according to the Riemannian volume. In particular, our results apply to Grassmann varieties and quadric hypersurfaces. The proof uses exponential mixing in the space of lattices and tools from geometry of numbers.

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  1. A century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard

    math.NT 2025-05 conditional novelty 2.0 of 10

    A survey of Khintchine's theorem and related results, with a simplified proof sketch of the Duffin-Schaeffer conjecture as proven by Koukoulopoulos and Maynard.

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