Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Zeros of some level 2 Eisenstein series

Authors: Sharon Garthwaite, Ling Long, Holly Swisher and Stephanie Treneer
Journal: Proc. Amer. Math. Soc. 138 (2010), 467-480
MSC (2000): Primary 11F11; Secondary 11F03
Published electronically: October 6, 2009
MathSciNet review: 2557165
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ \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 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F11, 11F03

Retrieve articles in all journals with MSC (2000): 11F11, 11F03

Additional Information

Sharon Garthwaite
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837

Ling Long
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011

Holly Swisher
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97301

Stephanie Treneer
Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225

Received by editor(s): June 4, 2009
Published electronically: October 6, 2009
Additional Notes: The second author was supported in part by the NSA grant no. H98230-08-1-0076.
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society