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Computation of
admissible Arakelov–Green functions on metrized graphs
Ruben Merlijn van Dijk and Enis Kaya |
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Vol. 19 (2026), No. 3, 491–516
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DOI: 10.2140/involve.2026.19.491
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Abstract |
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Metrized graphs are nonarchimedean analogues of Riemann surfaces, and Arakelov–Green functions on these graphs are of fundamental importance. In the present paper, we give an explicit formula for an admissible Arakelov–Green function on a metrized graph. 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
metrized graphs, metric graphs, Arakelov–Green functions,
algorithms
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Mathematical Subject Classification
Primary: 14G40, 90C35
Secondary: 14C17, 37P30
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Milestones
Received: 7 October 2024
Revised: 4 January 2025
Accepted: 13 February 2025
Published: 12 June 2026
Communicated by Kenneth S. Berenhaut
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Authors |
| Ruben Merlijn van Dijk | |
| Bernoulli Institute University of Groningen Groningen Netherlands |
Department of Digital Security Radboud University Nijmegen Netherlands |
| Enis Kaya | |
| Department of Mathematics Bilkent University Ankara Turkey |
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| © 2026 MSP (Mathematical Sciences Publishers). |
