Taylor expansion of an Eisenstein series

Yang, Tonghai

doi:10.1090/S0002-9947-03-03194-5

Taylor expansion of an Eisenstein series
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by Tonghai Yang PDF

Trans. Amer. Math. Soc. 355 (2003), 2663-2674 Request permission

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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