Department of Mathematics, Columbia University, New York, NY 10027.
Proc Natl Acad Sci U S A. 1984 Nov;81(22):7261-5. doi: 10.1073/pnas.81.22.7261.
This paper is devoted to the study of the arithmetic properties of values of G-functions introduced by Siegel [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1]. One of the main results is a theorem on the linear independence of values of G-functions at rational points close to the origin. In this theorem, no conditions are imposed on the p-adic convergence of a G-function at a generic point. The theorem finally realizes Siegel's program on G-function values outlined in his paper.
本文致力于研究由西格尔 [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] 引入的 G 函数值的算术性质。主要结果之一是关于原点附近有理点的 G 函数值的线性无关性的定理。在这个定理中，没有对 G 函数在一般点的 p-进收敛性施加任何条件。该定理最终实现了西格尔在其论文中概述的关于 G 函数值的计划。
