论文标题
舍纽型猜想和不一致
Schanuel Type Conjectures and Disjointness
论文作者
论文摘要
考虑到$ \ mathbb {c} $的子场$ f $，我们研究了由$ \ Overline {f} $的元素产生的字段$ e $的线性脱节，以及在Schanuel的猜想的情况下，由迭代对数产生的字段$ l $。在适当的版本的Schanuel猜想下，我们还获得了类似的结果，用模块化$ j $函数代替$ \ exp $，在$ \ mathbb {c} $上，线性的脱节是由$ \ mathrm {gl} _2 $的动作所取代的。我们还表明，对于$ f $的某些选择，我们获得了这些陈述的无条件版本。
Given a subfield $F$ of $\mathbb{C}$, we study the linear disjointess of the field $E$ generated by iterated exponentials of elements of $\overline{F}$, and the field $L$ generated by iterated logarithms, in the presence of Schanuel's conjecture. We also obtain similar results replacing $\exp$ by the modular $j$-function, under an appropriate version of Schanuel's conjecture, where linear disjointness is replaced by a notion coming from the action of $\mathrm{GL}_2$ on $\mathbb{C}$. We also show that for certain choices of $F$ we obtain unconditional versions of these statements.
