Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-Archimedean metric Mahler measure   Recently, Dubickas and Smyth constructed and examined the metric Mahler
measure and the metric na\"ive height on the multiplicative group of algebraic
numbers. We give a non-Archimedean version of the metric Mahler measure,
denoted $M_\infty$, and prove that $M_\infty(\alpha) = 1$ if and only if
$\alpha$ is a root of unity. We further show that $M_\infty$ defines a
projective height on $\bar{\mathbb Q}^\times/ \bar{\mathbb
Q}^\times_\mathrm{tors}$ as a vector space over $\mathbb Q$. Finally, we
demonstrate how to compute $M_\infty(\alpha)$ when $\alpha$ is a surd.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th