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arXiv · 2208.05857

Computation of Admissible Arakelov-Green Functions on Metrized Graphs

Ruben Merlijn van Dijk·Enis Kaya
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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.

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Ruben Merlijn van Dijk, Enis Kaya. 2022-08-11. Computation of Admissible Arakelov-Green Functions on Metrized Graphs. https://doi.org/10.2140/involve.2026.19.491

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