English

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 nn points on a Riemann surface, which grows asymptotically like O((logn)/n)O((\log n)/n). 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!