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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Taylor expansion of an Eisenstein series


Author: Tonghai Yang
Journal: Trans. Amer. Math. Soc. 355 (2003), 2663-2674
MSC (2000): Primary 11G05, 11M20, 14H52
Published electronically: February 27, 2003
MathSciNet review: 1975394
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Abstract: In this paper, we give an explicit formula for the first two terms of the Taylor expansion of a classical Eisenstein series of weight $2k+1$ for $\Gamma_{0}(q)$. Both the first term and the second term have interesting arithmetic interpretations. We apply the result to compute the central derivative of some Hecke $L$-functions.


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Additional Information

Tonghai Yang
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: thyang@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03194-5
PII: S 0002-9947(03)03194-5
Keywords: Kronecker formula, central derivative, elliptic curves, Eisenstein series
Received by editor(s): September 9, 2002
Published electronically: February 27, 2003
Additional Notes: Partially supported by an AMS Centennial fellowship and NSF grant DMS-0070476.
Article copyright: © Copyright 2003 American Mathematical Society