Document Type
Article
Publication Date
2010
Keywords
Zeros, 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 Γ(2) because of its elegant connection to a classical Jacobi elliptic function cn(u) which satisfies a differential equation (see formula (1.2)). 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.
Publication Title
Proceedings of the American Mathematical Society
Volume
138
First Page
467
Last Page
480
DOI
10.1090/S0002-9939-09-10175-2
Required Publisher's Statement
Proceedings of the American Mathematical Society allows the archiving of post prints to open access respositories. This article was published green open access and is free to the public five years after publication.
Recommended Citation
Garthwaite, Sharon; Long, Ling; Swisher, Holly; and Treneer, Stephanie, "Zeros of Some Level 2 Eisenstein Series" (2010). Mathematics Faculty Publications. 106.
https://cedar.wwu.edu/math_facpubs/106
Subjects - Topical (LCSH)
Eisenstein series; Jacobi forms
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Language
English
Format
application/pdf
