Transcendental constants over the coefficient fields in differential elliptic function fields

Abstract

Let A; be a differential field of characteristic 0, and be a universal extension of k. Suppose that the field of constants k 0 of k is algebraically closed. Consider the following differential polynomial of the first order over & in a single indeterminate y: T(y) = (y'V -S(y; *) e k ; O; here S(y; K) = y(ly)(l z y) ek; ic 2 0,1; *' = 0 .