Contribution to Book
Zeros of Classical Eisenstein Series and Recent Developments
Win-- women in numbers : research directions in number theory
(2011)
Abstract
In this survey, we begin by recalling a beautiful result of F. K. C. Rankin and Swinnerton-Dyer on the location of zeros of the classical Eisenstein series Ek (z) for the full modular group. We then explore more recent studies which have built upon this work to analyze the behavior of zeros of Ek (z), such as work by Nozaki on their separation property. We also review similar results for other classes of modular forms as well as zeros of Eisenstein series for different groups.We conclude with some results of the authors for a family of odd weight Eisenstein series on Γ(2), a prototypical genus zero subgroup with a simple fundamental domain.
Keywords
- Eisenstein series,
- Number theory
Disciplines
Publication Date
2011
Editor
Alina Carmen Cojocaru
Publisher
American Mathematical Society
Series
Fields Institute Communications
Publisher Statement
Providence, R.I. : American Mathematical Society ; Toronto, Canada : Fields Institute for Research in Mathematical Sciences
Citation Information
Sharon Anne Garthwaite, Stephanie Treneer, Ling Long and Holly Swisher. "Zeros of Classical Eisenstein Series and Recent Developments" Providence, R.I.Win-- women in numbers : research directions in number theory Vol. 60 (2011) p. 251 - 263 Available at: http://works.bepress.com/stephanie-treneer/7/