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- W2952173815 abstract "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." @default.
- W2952173815 created "2019-06-27" @default.
- W2952173815 creator A5058128142 @default.
- W2952173815 date "2011-05-24" @default.
- W2952173815 modified "2023-09-27" @default.
- W2952173815 title "Explicit bounds for sums of squares" @default.
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