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3 votes
0 answers
60 views

What circumstances guarantee a p-adic affine conjugacy map will be a rational function?

Let $\Bbb Q_p$ be a p-adic field and let any element $x$ of $\Bbb Q_p$ be associated with a unique element of $\Bbb Z_p$ via the quotient / equivalence relation $\forall n\in\Bbb Z:p^nx\sim x$ Then in ...
Robert Frost's user avatar
3 votes
0 answers
198 views

Characterizing rational functions on $\mathbb{Q}$ in terms of smooth extensions to $\mathbb{R}$ and $\mathbb{Q}_p$

Consider a function $f$ from a cofinite subset of $\mathbb{Q}$ to $\mathbb{Q}$. As established here and here $f$ extending to a smooth function on a cofinite subset of $\mathbb{R}$ is not sufficient ...
James E Hanson's user avatar