The derivative of an incoherent Eisenstein series. (English) Zbl 1275.11077
Let \(K= \mathbb Q (\sqrt{-D})\) be an imaginary quadratic field with discriminant \(-D <0\), and let \((V, q) = (K, -{\mathbf N})\) be the associated two-dimensional quadratic space over \(\mathbb Q\). Then an incoherent Eisenstein series on \(\mathrm{SL}(2, \mathbb A)\) is attached to an incoherent collection of local quadratic spaces coming from \((V,q)\). In this paper the author proves that each nonconstant Fourier coefficient of the derivative of this Eisenstein series can be expressed as the degree of certain zero cycles of a moduli scheme. This result generalizes previous work of Kudla, Rapoport and Yang.
Reviewer: Min Ho Lee (Cedar Falls)
MSC:
| 11F30 | Fourier coefficients of automorphic forms |
| 11F37 | Forms of half-integer weight; nonholomorphic modular forms |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
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