Let k be a differential
field of characteristic 0, and Ω be a universal extension of k. Suppose that
the field of constants k_{0} of k is algebraically closed. Consider the following
dlfferential polynomial of the first order over k in a single indeterminate
y:
here
Take a generic point z of the general solution of T. Then, z is transcendental over k,
and k(z,z′) is called a differential elliptic function field.
We prove the following:
Theorem. Let k(z,z′) be a differential elliptic function field over k. Then, there
exists a finitely generated differential extension field k^{∗} of k such that the following
three conditions are satisfied:
 z is transcendental over k^{∗};
 the field of constants of k^{∗} is the same as k_{0};
 there exists an element ζ of Ω such that k^{∗}(z,z′) = k^{∗}(ζ,ζ′) and (ζ′)^{2} =
4S(ζ;κ) with the same modulus as κ.
