A transcendence result on elliptic functions using functions of two variables

Abstract

Let ℘ be a Weierstrass ℘-function with algebraic g 2 and g 3 , whose fundamental periods ω 1 , ω 2 satisfy Im(ω 1 ) = 0. We show that πr or ℘(ω 1 r) is transcendental for any non-zero real number r.