All Questions
Tagged with p-adic-numbers nt.number-theory
105 questions
7
votes
1
answer
354
views
$(\varphi, \Gamma)$-modules of finite height
Maybe the answer to my question is obvious.
Let $p$ be a prime $\geq 3$. Let $D$ be an étale $(\varphi, \Gamma)$-module over $A_{\mathbb{Q}_p} = \{ \sum_{n \in \mathbb{Z}} a_n X^n \, \vert \, a_n \in ...
- 477
7
votes
2
answers
1k
views
Algebraic $p$-adic integers mod $p$
In studying the papers of Abbes and Saito on ramification theory in the imperfect residue field case, I come to the following questions. Let $\overline{\mathbb{Q}}_p\supset\mathbb{Q}{}^{t}_p\supset \...
- 4,492
3
votes
1
answer
499
views
Trivial p-adic measures
I am looking at p-adic distributions, and in this case p-adic measures. To say that $\mu$ is a distribution means that the arguments of $\mu$ are compact open subsets of $\mathbb{Z}_p$, $\mu$ is ...
- 43
32
votes
2
answers
3k
views
Does the equation $1 + 2 + 3 + \dots = -\frac{1}{12}$ have a natural $p$-adic interpretation?
Consider the equation
$$1 + 2 + 3 + 4 + \cdots = - \frac{1}{12},$$
"proved" by Ramanujan Euler. One correct way to interpret this is that $\zeta(-1) = - \frac{1}{12},$ where $\zeta(s) = \sum_{n = 1}^{\...
- 7,347
7
votes
0
answers
487
views
The character of a separable degree-$p$ extension of a local field of residual characteristic $p$ ?
Let $p$ be a prime number and $F$ a finite extension of ${\mathbf Q}_p$ or of ${\mathbf F}_p((t))$. I'm going to define a natural map from the set ${\mathcal S}_p(F)$ of degree-$p$ separable ...
- 18.7k