Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the image of $p$-adic logarithm   The objective of the paper is to explicitly compute the images of the maximal
ideals in the finite extensions of $p$-adic field $\mathbb{Q}_p$ under p-adic
logarithm. We have computed the image of the maximal ideal $\mathfrak{m}_K=\pi
\mathcal{O}_K$ of the ring $\mathcal{O}_K$ in the finite cyclotomic extension
$\mathbb{Q}_p(\zeta_p)$. We have identified the image of the contour region
$(1+\mathfrak{m}_K)\setminus (1+\mathfrak{m}_K^2)$ in the cyclotomic extension
$\mathbb{Q}_p(\zeta_p)$. Finally, we have introduced a technique using Newton
polygon to compute the images of maximal ideals of the $7$ quadratic extensions
of $\mathbb{Q}_2$ under $2$-adic logarithm.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph