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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Lindemann theorem for Artin-Hasse exponential

Consider the Dwork exponential $E(x)=\exp(\pi(x-x^p))$ with $\pi=\sqrt[p-1]{-p}$. It is well known that $E(1)=\gamma_p$ a $p$-th root of $1$ and hence not transcendant.
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