Distribution of rational points on random Fano hypersurfaces

2023/10/20 by Yohsuke Matsuzawa, Yuta Suzuki, Matsuzawa, Yohsuke +1
Mathematics · #14G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary: 11D45 #Secondary: 11P21 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2310.13408

openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an asymptotic formula for the average number of rational points on Fano hypersurfaces that are contained in a small ball centered at a given adelic point. We also prove an asymptotic formula for the number of hypersurfaces admitting adelic points that are contained in a small ball.

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