A transcendence result on elliptic functions using functions of two variables

Abstract

Let $\wp$ be a Weierstrass $\wp$-function with algebraic $g_2$ and $g_3$, which has a non-zero real period $\omega$. We show that at least one of $\pi r$ and $\wp (\omega r)$ is transcendental for any non-zero real number $r$.

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References in corpus (1)

• Meromorphic function fields closed by partial derivatives