超越函数的代数值

关于代数点的名称或超越代数值的解析函数

Sur le nombre de points algebriques ou une fonction analytique transcendante prend des valeurs algebriques

研究了解析超越函数取代数值的高度和次数有界的代数数的集合。

Relations algébriques entre valeurs de E-fonctions ou de M-fonctions

We prove that all algebraic relations over $\overline{\mathbb Q}$ between values of Siegel's $E$-functions at some non-zero algebraic point have a functional source, in that they can be obtained as degeneration of $δ$-algebraic relations over $\overline{\mathbb Q}(z)$ between the functions at stake. We also obtain an analogous result when considering Mahler's $M_q$-functions. In this case, the so-called $σ_q$-algebraic relations substitute for the $δ$-algebraic relations. We also give several consequences of this result concerning some descent phenomena. The point of view we adopt here reveals…