Mathematics – Number Theory
Scientific paper
2009-08-24
Mathematics
Number Theory
14 pages, 1 figure
Scientific paper
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.
Garthwaite Sharon
Long Ling
Swisher Holly
Treneer Stephanie
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