A Mahler-type estimate of weighted Fekete sums on the Berkovich projective line

TL;DR

This paper develops a Mahler-type estimate for weighted Fekete sums on the Berkovich projective line over algebraically closed fields with possibly positive characteristic and non-archimedean absolute values.

Contribution

It introduces a new Mahler-type estimate applicable to weighted Fekete sums in the Berkovich setting, extending classical results to non-archimedean and positive characteristic contexts.

Findings

Establishment of a Mahler-type inequality for weighted Fekete sums

Extension of classical estimates to Berkovich projective line over non-archimedean fields

Applicability to fields with positive characteristic

Abstract

We establish a Mahler-type estimate of weighted Fekete sums on the Berkovich projective line over an algebraically closed field of possibly positive characteristic that is complete with respect to a non-trivial and possibly non-archimedean absolute value.