Quadratic residue patterns and point counting on K3 surfaces

2023/03/06 by Valentina Kiritchenko, Mikhail Tsfasman, Kiritchenko, Valentina +5
Mathematics · #01A60 (Secondary) #11A15 (Primary) #14A15 (Secondary) 01A55 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.03270

openalex publication_date 2023/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quadratic residue patterns modulo a prime are studied since 19th century. We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of algebraic geometry, and prove it. The core of this theorem is an unexpected relation between the number of points on a K3 surface and that on a CM elliptic curve.

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