An alternative proof of the Faltings-Elkies bound
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(( 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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