Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear independence of values of logarithms revisited   Let $m\ge 2$ be an integer, $K$ an algebraic number field and $\alpha\in
K\setminus \{0,-1\}$ with sufficiently small absolute value. In this article,
we provide a new lower bound for linear form in
$1,{\rm{log}}(1+\alpha),\ldots,{\rm{log}}^{m-1}(1+\alpha)$ with algebraic
integer coefficients in both complex and $p$-adic cases (see Theorem $2.1$ and
Theorem $2.4$). Especially, in the complex case, our result is a refinement of
the result of Nesterenko-Waldschmidt on the lower bound of linear form in
certain values of power of logarithms. The main integrant is based on
Hermite-Mahler's Pad\'{e} approximation of exponential and logarithm functions.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn