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arXiv · 1207.2949

Special values of canonical Green's functions

Robin de Jong
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Abstract

We give a precise formula for the value of the canonical Green's function at a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we express the 'energy' of the Weierstrass points in terms of a spectral invariant recently introduced by N. Kawazumi and S. Zhang. It follows that the energy is strictly larger than log 2. Our results generalize known formulas for elliptic curves.

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Robin de Jong. 2012-07-12. Special values of canonical Green's functions. https://doi.org/10.1007/s00209-012-1064-2

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