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arXiv · 2310.03648

An alternative proof of the Faltings-Elkies bound

Robert Wilms
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Abstract

We give an alternative proof of the Faltings-Elkies bound on the average value of the Arakelov-Green function in pairs of a given set of $n$ points on a Riemann surface, which grows asymptotically like $O((\log n)/n)$. Our result is effective in terms of bounds of the Arakelov-Green function with respect to a given covering by local coordinates.

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Robert Wilms. 2023-10-05. An alternative proof of the Faltings-Elkies bound. https://arxiv.org/abs/2310.03648

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