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arXiv · 2105.14868

Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field

Kaloyan Slavov
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Abstract

We sharpen to nearly optimal the known asymptotic and explicit bounds for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinatorial technique. Namely, we study the number of $\mathbb{F}_q$-points on the intersection of the given hypersurface with a random plane.

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Kaloyan Slavov. 2021-05-31. Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field. https://doi.org/10.4153/s0008439522000625

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