Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of a theorem of Boyd and Lawton   The Mahler measure of a nonzero $n$-variable polynomial $P$ is the integral
of $\log|P|$ on the unit $n$-torus. A result of Boyd and Lawton says that the
Mahler measure of a multivariate polynomial is the limit of Mahler measures of
univariate polynomials. We prove the analogous result for different extensions
of Mahler measure such as generalized Mahler measure (integrating the maximum
of $\log|P|$ for possibly different $P$'s), multiple Mahler measure (involving
products of $\log|P|$ for possibly different $P$'s), and higher Mahler measure
(involving $\log^k|P|$).

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph