# Tagged Questions

**8**

votes

**1**answer

210 views

### is there a p-adic implicit function theorem?

I am trying to find a good reference for a version of the implicit function theorem over $p$-adic manifolds. None of the texts I have consulted ( including "$p$-adic numbers, $p$-adic analysis, and ...

**4**

votes

**1**answer

172 views

### Iwasawa logarithm and analytic continuation

I am reading Number Theory vol. 1 by Henri Cohen (among other things) and I am curious about the Iwasawa logarithm. Let $\mathbb{C}_p$ be the completion of the algebraic closure of $\mathbb{Q}_p$.
...

**2**

votes

**0**answers

114 views

### Transcendental numbers in the p-adic rationals $\mathbb Q_p$ [closed]

I know that there are uncountably infinite transcendentals over $\mathbb Q$ in $\mathbb Q_p$. What i want to ask is if there is a way to determine whether a transcendental over $\mathbb Q$ lays in ...

**0**

votes

**0**answers

230 views

### What is $p$-adic Fourier series?

Q1: Can we define Fourier series for a function $\mathbb{Z}_p\to \mathbb{Q}_p$?
Q2: There are (in a real case) Bernoulli polynomials which have the most simple Fourier expansion:
...

**5**

votes

**0**answers

199 views

### 2-adic Logarithm and Resistance of n-dimensional Cube

Resistance across opposite vertices of n-dimensional cube with each edge at one ohm resistance is
$$R_n=\sum_{k=0}^{n-1}\frac1{(n-k){n\choose k}}=\frac1n\sum_{k=1}^{n}\frac1{{n-1\choose k}}.$$
The ...

**2**

votes

**1**answer

219 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 ...

**1**

vote

**0**answers

165 views

### p-adic Lie theory

It is well known that exponential map in $C^{n\times n}$ will cover all non-sigular matrix $GL(n,C)$, which is a basic fact in Lie group and lie algebra theory, whether it is true for p-adic cases.
...

**6**

votes

**0**answers

242 views

### Differences in tree picture of ${\bf Q}_p$, $\overline{{\bf Q}_p}$, ${\bf C}_p$, $\Omega_p$

I was discussing the tree picture of ${\bf Z}_p$ and ${\bf Q}_p$ and mentioned that the idea can be extended to ${\bf C}_p$, with the caveat that the tree is no longer locally finite (as the value ...

**0**

votes

**0**answers

111 views

### the definition of pro-infinitesimal thickenings

Let $R$ be a ring and $A$ and $R$-algebra. A pro-infinitesimal thickening of $R$ is a pair $(D, \theta)$ such that $\theta: D \rightarrow R$ is surjective and $D$ is separated and complete for the ...

**4**

votes

**0**answers

444 views

### Newton Method in $p$-adic case

The Newton Method over $\mathbb{R}$ has the property that the precision is doubled (under some continuous differentialbe assumption) in each iteration. For the ring $\mathbb{Z}_p$ of $p$-adic ...

**1**

vote

**1**answer

234 views

### Partitioning a compact open set into balls in an ultrametric space

Consider a $p$-adic field $K$ with the standard topology inherited from the usual $p$-adic norm $\mid \cdot \mid$. Consider the ultrametric space $X=K^n$ with the topology inherited from the norm $\| ...