Bounds for coefficients of cusp forms and extremal lattices

Details Bounds for coefficients of cusp forms and extremal lattices Bounds for coefficients of cusp forms and extremal lattices

2010-12-29

arxiv.org/abs/1012.5991v2

Bull. London Math. Soc., 43 (2011), no. 5, 927-938

Mathematics

Number Theory

To appear in Bulletin of the London Mathematical Society

Scientific paper

10.1112/blms/bdr030

A cusp form $f(z)$ of weight $k$ for $\SL_{2}(\Z)$ is determined uniquely by its first $\ell := \dim S_{k}$ Fourier coefficients. We derive an explicit bound on the $n$th coefficient of $f$ in terms of its first $\ell$ coefficients. We use this result to study the non-negativity of the coefficients of the unique modular form of weight $k$ with Fourier expansion \[F_{k,0}(z) = 1 + O(q^{\ell + 1}).\] In particular, we show that $k = 81632$ is the largest weight for which all the coefficients of $F_{0,k}(z)$ are non-negative. This result has applications to the theory of extremal lattices.

Affiliated with

Also associated with

No associations

Rating

Bounds for coefficients of cusp forms and extremal lattices 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 Bounds for coefficients of cusp forms and extremal lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bounds for coefficients of cusp forms and extremal lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-611468