On zeros of Eisenstein series for genus zero Fuchsian groups

Author:
Heekyoung Hahn

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2391-2401

MSC (2000):
Primary 11F03, 11F11

DOI:
https://doi.org/10.1090/S0002-9939-07-08763-1

Published electronically:
March 29, 2007

MathSciNet review:
2302560

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let SL be a genus zero Fuchsian group of the first kind with as a cusp, and let be the holomorphic Eisenstein series of weight on that is nonvanishing at and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on and on a choice of a fundamental domain , we prove that all but possibly of the nontrivial zeros of lie on a certain subset of . Here is a constant that does not depend on the weight, is the upper half-plane, and is the canonical hauptmodul for

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Additional Information

**Heekyoung Hahn**

Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627

Email:
hahn@math.rochester.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-08763-1

Keywords:
Eisenstein series,
modular forms,
divisor polynomials

Received by editor(s):
March 21, 2006

Received by editor(s) in revised form:
April 27, 2006

Published electronically:
March 29, 2007

Additional Notes:
This research was supported in part by a National Science Foundation FRG grant (DMS 0244660)

Communicated by:
Ken Ono

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.