Zeros of some level 2 Eisenstein series
Authors:
Sharon Garthwaite, Ling Long, Holly Swisher and Stephanie Treneer
Journal:
Proc. Amer. Math. Soc. 138 (2010), 467480
MSC (2000):
Primary 11F11; Secondary 11F03
Published electronically:
October 6, 2009
MathSciNet review:
2557165
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Abstract 
References 
Similar Articles 
Additional Information
Abstract: The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and SwinnertonDyer 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 because of its elegant connection to a classical Jacobi elliptic function 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 series.
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Additional Information
Sharon Garthwaite
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
Email:
sharon.garthwaite@bucknell.edu
Ling Long
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email:
linglong@iastate.edu
Holly Swisher
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97301
Email:
swisherh@math.oregonstate.edu
Stephanie Treneer
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email:
stephanie.treneer@wwu.edu
DOI:
http://dx.doi.org/10.1090/S0002993909101752
PII:
S 00029939(09)101752
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. H982300810076.
Communicated by:
Ken Ono
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
