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arXiv · 2211.09556

Schanuel Type Conjectures and Disjointness

Isaac A. Broudy·Sebastian Eterović
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Abstract

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.

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Isaac A. Broudy, Sebastian Eterović. 2022-11-17. Schanuel Type Conjectures and Disjointness. https://arxiv.org/abs/2211.09556

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