Explicit bounds for sums of squares

Details Explicit bounds for sums of squares Explicit bounds for sums of squares

2011-05-24

arxiv.org/abs/1105.4824v1

Mathematics

Number Theory

21 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Explicit bounds for sums of squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit bounds for sums of squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit bounds for sums of squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-516827