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Taylor expansion of an Eisenstein series

Author(s): Tonghai Yang
Journal: Trans. Amer. Math. Soc. 355 (2003), 2663-2674.
MSC (2000): Primary 11G05, 11M20, 14H52
Posted: February 27, 2003
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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: 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
Posted: February 27, 2003
Additional Notes: Partially supported by an AMS Centennial fellowship and NSF grant DMS-0070476.
Copyright of article: Copyright 2003, American Mathematical Society

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