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Local interdefinability of Weierstrass elliptic functions

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Introduction to Elliptic Curves

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Galois Groups of Difference Equations of Order Two on Elliptic Curves

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Model theory of elliptic functions

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. I'm sorry if my question is trivial. In his book "Elements of the Theory of Elliptic Functions", page 44, Akhiezer proves, that any two elliptic functions with the same periods are connected by an algebraic relation. What is meant by the word "eliminate"?

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There are three fundamental facts in play here. Lemma I. This is repeated in Theorem 2 here. Lemma II. This is the subject of this MSE question. It is known as the transcendence degree. It is analogous to the invariant of a dimension for vector spaces the size of a basis is independent of which basis is chosen.

This implies the extension has transcendence degree equal to one. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. An algebraic relation between any two elliptic functions with the same periods Ask Question.


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