An alternative proof of the Faltings-Elkies bound
Algebraic Geometry
2023-10-06 v1 Number Theory
Abstract
We give an alternative proof of the Faltings-Elkies bound on the average value of the Arakelov-Green function in pairs of a given set of points on a Riemann surface, which grows asymptotically like . Our result is effective in terms of bounds of the Arakelov-Green function with respect to a given covering by local coordinates.
Keywords
Cite
@article{arxiv.2310.03648,
title = {An alternative proof of the Faltings-Elkies bound},
author = {Robert Wilms},
journal= {arXiv preprint arXiv:2310.03648},
year = {2023}
}
Comments
11 pages. Comments are welcome!