منابع مشابه
Taylor Expansion of an Eisenstein Series
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 Γ0(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. 0. Introduction. Consider the classical Eisenstein series ∑ γ∈Γ∞\ SL2(Z) Im(γτ)...
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The leading term of Eisenstein series and L-functions are well-known to be extremely important and to have very important arithmetic implications. For example, one may consider the analytic class number formula, The Siegel-Weil formula, the Birch and Swinnerton-Dyer conjecture, Stark’s conjectures, and Beilinson’s and Bloch-Kato conjectures. These are well-documented and are central in current ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03194-5