Zeros of some level 2 Eisenstein series
Abstract
The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc of the fundamental domain, and recent work by Nozaki explores their interlacing property. In this paper we extend these distribution properties to a particular family of Eisenstein series on Gamma(2) because of its elegant connection to a classical Jacobi elliptic function cn(u) which satisfies a differential equation. As part of this study we recursively define a sequence of polynomials from the differential equation mentioned above that allow us to calculate zeros of these Eisenstein series. We end with a result linking the zeros of these Eisenstein series to an L-series.
Cite
@article{arxiv.0908.3511,
title = {Zeros of some level 2 Eisenstein series},
author = {Sharon Garthwaite and Ling Long and Holly Swisher and Stephanie Treneer},
journal= {arXiv preprint arXiv:0908.3511},
year = {2009}
}
Comments
14 pages, 1 figure