On zeros of Eisenstein series for genus zero Fuchsian groups
| dc.creator | Hahn, Heekyoung | |
| dc.date | 2006-03-27 | |
| dc.date.accessioned | 2026-07-07T07:07:15Z | |
| dc.date.available | 2026-07-07T07:07:15Z | |
| dc.description | Let $\GN\leq\SLR$ be a genus zero Fuchsian group of the first kind with $\infty$ as a cusp, and let $\Ek$ be the holomorphic Eisenstein series of weight $2k$ on $\GN$ that is nonvanishing at $\infty$ and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on $\GN,$ and on a choice of a fundamental domain $\F$, we prove that all but possibly $c(\GN,\F)$ of the non-trivial zeros of $\Ek$ lie on a certain subset of $\{z\in\mathfrak{H} : \JN(z)\in\mathbb{R}\}$. Here $c(\GN,\F)$ is a constant that does not depend on the weight $2k$ and $\JN$ is the canonical hauptmodul for $\GN.$ | |
| dc.identifier | https://arxiv.org/abs/math/0603625 | |
| dc.identifier | http://arxiv.org/abs/math/0603625 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110325 | |
| dc.subject | Number Theory | |
| dc.subject | 11F03; 11F11 | |
| dc.title | On zeros of Eisenstein series for genus zero Fuchsian groups | |
| dc.type | text |