Schanuel's conjecture and the exceptional set of $\gamma$-th arithmetic zeta functions

Abstract

In this work, we study the arithmetic nature of the numbers of the form $n^{\g}$, for $n\in \mathbb{N}$ and $\g\in \C$. We also consider a related conjecture and we show that it is a consequence of the unipresent Schanuel's conjecture.

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