Department of Mathematics, Columbia University, New York, NY 10027.
Proc Natl Acad Sci U S A. 1985 Apr;82(8):2212-6. doi: 10.1073/pnas.82.8.2212.
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.
我们使用 Padé 逼近方法证明了 Eisenstein 定理的一个逆定理，该定理涉及到代数函数展开式中系数分母的有界性，对于由亚纯函数参数化的函数类。这个结果被应用于 Tate 猜想，即对椭圆曲线的同态的有效描述。
