Computation of admissible Arakelov–Green functions on metrized graphs
Abstract
Metrized graphs are nonarchimedean analogues of Riemann surfaces, and Arakelov-Green functions on these graphs are of fundamental importance for some aspects of arithmetic geometry. In the present paper, we give an explicit formula for an admissible Arakelov-Green function on a metrized graph, extending Cinkir's formula for the canonical Arakelov-Green function. Based on our formula, we present and implement an algorithm in the computer algebra system SageMath for explicitly computing such functions. We illustrate our algorithm with computational examples.
Fields of Study & Subjects
advanced mathematical theories
Mathematical and Theoretical Analysis
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Involve a Journal of Mathematics
- Volume
- 19
- Issue
- 3
- Pages
- 491–516
- Publication date
- 12 June 2026
- Language
- EN