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Results tagged with p-adic-numbers
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user 26522
The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems
12
votes
Accepted
Mori: p-adic and real hemispheres of the mathematical universe?
As the night sky, mathematics has two hemispheres; the archimedean hemisphere and the non-archimedean hemisphere. For some reasons, the latter hemisphere is usually under the horizon of our world, …
- 13.8k
6
votes
Accepted
Transcendence of a ratio of p-adic logarithms
This is a typical case of the $p$-adic Four Exponentials conjecture. It is surely true, but the proof is beyond reach. If you add in a third prime (equality of $\log_p{x_i} / \log_p{\ell_i}$ for $i = …
- 13.8k
4
votes
0
answers
150
views
Finiteness of the set of $\mathbb{Q}_p$-rational periodic points
The statement I am concerned with is this:
Let $\varphi : \mathbb{P}^r_{\mathbb{Z}_p} \to \mathbb{P}^r_{\mathbb{Z}_p}$ be a morphism of degree higher than one. Then the set of $\mathbb{Q}_p$-rationa …
- 13.8k