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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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Totally ramified p-extension over $F_q((X))$
Let $K=F_q((X))$, from Artin-Schreier theory, for a cyclic extension $L/K$ of degree p, we have $L=K(x)$, $x^p-x=\alpha$. So when $L/K$ is totally ramified, could we find some $x$ s.t the correspondin …