Zeros, Eisenstein series
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.
Proceedings of the American Mathematical Society
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.
Garthwaite, Sharon; Long, Ling; Swisher, Holly; and Treneer, Stephanie, "Zeros of Some Level 2 Eisenstein Series" (2010). Mathematics. 106.
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 License