Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit bounds for sums of squares   For an even integer $k$, let $r_{2k}(n)$ be the number of representations of
$n$ as a sum of $2k$ squares. The quantity $r_{2k}(n)$ is appoximated by the
classical singular series $\rho_{2k}(n) \asymp n^{k-1}$. Deligne's bound on the
Fourier coefficients of Hecke eigenforms gives that $r_{2k}(n) = \rho_{2k}(n) +
O(d(n) n^{\frac{k-1}{2}})$. We determine the optimal implied constant in this
estimate provided that either $k/2$ or $n$ is odd. The proof requires a
delicate positivity argument involving Petersson inner products.

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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: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys