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p-adic numbers vs real numbers - Mathematics Stack Exchange
Jan 30, 2021 · Rather, one would have to investigate what "roles" the classical $\pi$ "plays" in the real numbers (e.g.: area and / or half the circumference of the unit circle; first positive zero of …
Method of finding a p-adic expansion to a rational number
Mar 12, 2015 · I'll give an answer that's more procedural. You can calculate the p-adic expansion for a given rational number using the following algorithm: Let a/b be a rational number, let p be …
Why introduce the $p$-adic numbers? - Mathematics Stack …
We find that the p-adic integers are formal neighborhoods of closed points in $\mathbb{Z}$, so they naturally show up in the deformation theory of arithmetic objects (Schemes over …
What is the characteristic of p-adic number fields?
Jun 5, 2018 · I want to know if the p-adic fields $\mathbb{Q}_p, \mathbb{Z}_p$ are characteristic 0 fields, or what are their characteristics? Actually, is $\mathbb{Z}_p$ a field at all? (note that the …
number theory - Understanding $p$-adic fields - Mathematics …
Jun 19, 2015 · It can be shown (Ostrowski's theorem) that Q admits only 2 distances which are compatible with + and x : the "archimedaean" one, built from the usual absolute value, and the …
Classical number theoretic applications of the $p$-adic numbers
Dec 16, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
History of $p$-adic numbers - Mathematics Stack Exchange
In the recent literature on the history of p-adic numbers, I found two references that "suspect" that Gauss had something similar to p-adic analysis in his arsenal: The article " on the origin of p …
Why are $p$-adic numbers and $p$-adic integers only defined for …
Sep 8, 2016 · It makes perfect sense to speak of a base $10$ digit expansion. Why does it not make sense to speak of $10$-adic numbers or $10$-adic integers?
$p$-adic Numbers Textbook Suggestions - Mathematics Stack …
Jul 19, 2020 · (1) p-adic Numbers: An Introduction by Fernando Q. Gouvêa (2) A Course in p-adic Analysis by Alain M. Robert (3) Introduction To p-adic Analytic Number Theory by M Ram …
reference request - A resource for learning p-adic numbers ...
Jun 30, 2022 · "P-adic Analysis compared with Real," by Svetlana Katok is a very gentle introduction to p-adic numbers. This text is suitable for an undergrad who has taken some …