On zeros of Eisenstein series for genus zero Fuchsian groups
Author:
Heekyoung Hahn
Journal:
Proc. Amer. Math. Soc. 135 (2007), 23912401
MSC (2000):
Primary 11F03, 11F11
Published electronically:
March 29, 2007
MathSciNet review:
2302560
Fulltext PDF Free Access
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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 halfplane, 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:
http://dx.doi.org/10.1090/S0002993907087631
PII:
S 00029939(07)087631
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.
