Quadratic residue patterns and point counting on K3 surfaces
Algebraic Geometry
2023-03-07 v1 Number Theory
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 We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of algebraic geometry, and prove it.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.
Keywords
Cite
@article{arxiv.2303.03270,
title = {Quadratic residue patterns and point counting on K3 surfaces},
author = {Valentina Kiritchenko and Mikhail Tsfasman and Serge Vladuts and Ilya Zakharevich},
journal= {arXiv preprint arXiv:2303.03270},
year = {2023}
}
Comments
9 pages, highly preliminary