Title

Zeros of some level 2 Eisenstein series

Document Type

Article

Publication Date

2-1-2010

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 Τ(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 allows us to calculate zeros of these Eisenstein series. We end with a result linking the zeros of these Eisenstein series to an L-series. © 2009 American Mathematical Society.

Publication Source (Journal or Book title)

Proceedings of the American Mathematical Society

First Page

467

Last Page

480

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