Dr Rajula Srivastava (Universität Bonn): Counting Rational Points near Flat Hypersurfaces

Thursday, 22.06.2023 14:15 im Raum M4

Mathematik und Informatik

How many rational points with denominator of a given size lie within a given distance from a compact hypersurface? In this talk, we shall describe how the geometry of the surface plays a key role in determining this count, and present a heuristic for the same. In a recent breakthrough, J.J. Huang proved that this guess is indeed true for hypersurfaces with non-vanishing Gaussian curvature. What about hypersurfaces with curvature only vanishing up to a finite order, at a single point? We shall offer a new heuristic in this regime which also incorporates the contribution arising from "local flatness". Further, we will describe how ideas from Harmonic Analysis can be used to establish the indicated estimates for hypersurfaces of this type immersed by homogeneous functions. Based on joint work with N. Technau.

Angelegt am Wednesday, 26.04.2023 17:17 von cauri_01
Geändert am Tuesday, 23.05.2023 09:25 von cauri_01
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