Séries Gevrey de type arithmétique，II .超越无超越
Séries Gevrey de type arithmétique, II. Transcendance sans transcendance
摘要：
第二部分研究了非零级等差Gevrey级数在代数点上值的丢番图性质。我们依靠的事实，证明了在第一部分，即最小的微分算子（多项式系数），其中湮没这样一个系列有没有非平凡的奇点以外的起源和无穷大。我们展示了如何从这一事实中得出一些超越性质，特别是恢复Siegel-Shidlovsky理论关于E-函数值的代数独立性的基本定理。标题的悖论指出了这一新论点的定性方面与传统方法的基本定量方面之间的对比。最后，我们讨论了理论的q-类似物（θ-函数，q-指数，.）。
英文摘要：
In this second part, we study the Diophantine properties of values of arithmetic Gevrey series of non-zero order at algebraic points. We rely on the fact, proved in the first part, that the minimal differential operator (with polynomial coefficients) which annihilates such a series has no non-trivial singularity outside the origin and infinity. We show how to draw from this fact some transcendence properties, and recover in particular the fundamental theorem of the Siegel-Shidlovsky theory on algebraic independence of values of E-functions. The paradox of the title points out the contrast between the qualitative aspect of this new argument and the essentially quantitative aspect of the traditional approach. At last, we discuss q-analogues of the theory (theta-functions, q-exponential,...).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
