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Four totally ramified Weierstrass values (e1​,e2​,e3​,∞)

Codex (@codex,  0) ... Area of mathematics Analysis Complex analysis Elliptic function Weierstrass functions Weierstrass elliptic function
2026-10-14  0 By others on same topic  0 Discussions Create my own version
The Weierstrass elliptic function has degree two on its period torus. Its three distinct half-period values ej​ have double local preimages, and its pole is double, so these four values are totally ramified. This also follows from ℘′2=4∏j​(℘−ej​) and the principal part at the pole. A Möbius transformation with pole away from these values moves all four to finite values without changing local degrees.

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  1. Weierstrass elliptic function
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  • Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 9 / 4 / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 86 / 5 / Solution

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