Zeros of the Eisenstein series $E_2$
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- by Abdelkrim El Basraoui and Abdellah Sebbar PDF
- Proc. Amer. Math. Soc. 138 (2010), 2289-2299 Request permission
Abstract:
In this paper we investigate the zeros of the Eisenstein series $E_2$. In particular, we prove that $E_2$ has infinitely many $\operatorname {SL}_2(\mathbb {Z})$-inequivalent zeros in the upper half-plane $\mathfrak {H}$, yet none in the standard fundamental $\mathfrak {F}$. Furthermore, we go on to investigate other fundamental regions in the upper half-plane $\mathfrak {H}$ for which there do or do not exist zeros of $E_2$. We establish infinitely many such regions containing a zero of $E_2$ and infinitely many which do not.References
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Additional Information
- Abdelkrim El Basraoui
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Email: asebbar@uottawa.ca
- Abdellah Sebbar
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Email: aelba026@uottawa.ca
- Received by editor(s): April 21, 2009
- Received by editor(s) in revised form: October 3, 2009
- Published electronically: February 24, 2010
- Communicated by: Keno Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2289-2299
- MSC (2010): Primary 11F11
- DOI: https://doi.org/10.1090/S0002-9939-10-10300-1
- MathSciNet review: 2607858