Transcendence of elliptic modular functions in characteristic p, by Jose' Felipe Voloch
This paper has appeared in J. Number Theory 58 (1996), no. 1, 55-59, and
so the dvi version has been removed. If K is a global field of positive characteristic and v is a place of K
where an elliptic curve E has split multiplicative reduction, then
the Tate parameter q of E is transcendental over K and so is any element
of the completion of K at v which maps to a point of infinite order in E(K)
under the Tate parametrization.
Jose' Felipe Voloch <email@example.com>