English

Explicit uniform estimate of arithmetic Hilbert-Samuel function of hypersurfaces

Algebraic Geometry 2018-08-13 v1 Number Theory

Abstract

In this paper, we will give an upper bound and a lower bound of the arithmetic Hilbert-Samuel function of projective hypersurfaces, which are uniform and explicit. These two bounds have the optimal dominant terms. As an application, we use the lower bound to get an estimate of the density of rational points with small heights in a hypersurface.

Keywords

Cite

@article{arxiv.1808.03451,
  title  = {Explicit uniform estimate of arithmetic Hilbert-Samuel function of hypersurfaces},
  author = {Chunhui Liu},
  journal= {arXiv preprint arXiv:1808.03451},
  year   = {2018}
}

Comments

45 pages

R2 v1 2026-06-23T03:29:43.848Z