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The valuative capacity of the set of sums of $d$-th powers | Marie-Andree B.Langlois
; | Date: |
1 Sep 2016 | Abstract: | 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 $lim_{n o
infty}frac{alpha_{E,p}(n)}{n}$ 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. | Source: | arXiv, 1609.0299 | Services: | Forum | Review | PDF | Favorites |
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