English

Computation of Admissible Arakelov-Green Functions on Metrized Graphs

Algebraic Geometry 2022-08-12 v1 Combinatorics Number Theory

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.

Keywords

Cite

@article{arxiv.2208.05857,
  title  = {Computation of Admissible Arakelov-Green Functions on Metrized Graphs},
  author = {Ruben Merlijn van Dijk and Enis Kaya},
  journal= {arXiv preprint arXiv:2208.05857},
  year   = {2022}
}

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