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