Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The valuative capacity of the set of sums of $d$-th powers   If $E$ is a subset of the integers then the $n$-th characteristic ideal of
$E$ is the fractional ideal of $\mathbb{Z} $ consisting of $0$ and the leading
coefficients of the polynomials in $\mathbb{Q}[x]$ of degree no more than $n$
which are integer valued on $E$. For $p$ a prime the characteristic sequence of
$Int(E,\mathbb{Z})$ is the sequence $\alpha_E (n)$ of negatives of the $p$-adic
valuations of these ideals. The asymptotic limit $\lim_{n\to
\infty}\frac{\alpha_{E,p}(n)}{n}$ of this sequence, called the valuative
capacity of $E$, gives information about the geometry of $E$. We compute these
valuative capacities for the sets $E$ of sums of $\ell \geq 2$ integers to the
power of $d$, by observing the $p$-adic closure of these sets.

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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess