Derivatives of Eisenstein series and Faltings heights
نویسندگان
چکیده
منابع مشابه
Derivatives of Eisenstein series and Faltings heights
In a series of papers, [25], [30], [28], [29], [31], [26], we showed that certain quantities from the arithmetic geometry of Shimura varieties associated to orthogonal groups occur in the Fourier coefficients of the derivative of suitable Siegel-Eisenstein series. It was essential in these examples that this derivative was the second term in the Laurent expansion of a Siegel-Eisenstein series a...
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This function can be obtained, via analytic continuation, as a special value of an Eisenstein series E(τ, s) at s = 12 . In this note, we will give an arithmetic interpretation to Zagier’s Eisenstein series and its derivative at s = 12 , using Arakelov theory. Let M be the Deligne–Rapoport compactification of the moduli stack over Z of elliptic curves [DR]. In Section 3 we will define a generat...
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ignoring many important details and serious technical problems in the process. I apologize at the outset for the very speculative nature of the picture given here. I hope that, in spite of many imprecisions, the sketch will provide a context for a variety of particular cases where precise results have been obtained. Recent results on one of these, part of an ongoing joint project with Michael R...
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We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties M associated to rational quadratic forms (V,Q) of signature (n, 2). In the case n = 1, we define generating series φ̂1(τ ) for 1-cycles (resp. φ̂2(τ ) for 0-cycles) on the arithmetic surface M associated to a Shimura curve over Q. These ...
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In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at s = 2. Here we derive an infinite family of formulas which includes Ramanujan’s original formula as a special case. Our results depend on a representation of values of the derivatives of Dirichlet ...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2004
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x03000459