A transcendence result on elliptic functions using functions of two variables

Let $\mathrm{\wp }$ be a Weierstrass $\mathrm{\wp }$-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$\wp(\omega r)$istranscendentalforanynon-zerorealnumber$r$.