Abstract
Given a compact Riemann surface S of genus g ≥ 2, one says that a point p ∈ s is a Weierstrass point if there exists a differential of the first kind on S, different from 0, which vanishes at p to order at least g. The set of Weierstrass points on S is nonempty and finite; indeed, each Weierstrass point is assigned a positive integer called the Weierstrass weight, and then one has the result that the sum of the weights of all Weierstrass points on S is (g−l)g(g+l).
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Rohrlich, D.E. (1982). Some Remarks on Weierstrass Points. In: Koblitz, N. (eds) Number Theory Related to Fermat’s Last Theorem. Progress in Mathematics, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6699-5_5
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DOI: https://doi.org/10.1007/978-1-4899-6699-5_5
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