By David Ginzburg, Erez Lapid, David Soudry
This ebook is the second one of 2 volumes, which characterize major issues of present learn in automorphic types and illustration conception of reductive teams over neighborhood fields. Articles during this quantity ordinarily signify worldwide facets of automorphic kinds. one of the subject matters are the hint formulation; functoriality; representations of reductive teams over neighborhood fields; the relative hint formulation and classes of automorphic kinds; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions. The articles are written through major researchers within the box, and convey the reader, complicated graduate scholars and researchers alike, to the frontline of the full of life study in those deep, important subject matters. The significant other quantity (""Contemporary arithmetic, quantity 488"") is dedicated to worldwide points of automorphic varieties
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Extra resources for Automorphic Forms and L-functions II: Local Aspects
This type of Eisenstein series was studied by Klingen [Kl67] and then generalized by Arakawa [Ara83] to the vector-valued case. Remarks. Remark 1. The Dirichlet series φ(d)λ(d)ρ d−k−2s in the formula above can be rephrased in terms of the symmetric square L-function attached to f1 . Remark 2. In the general case (N 2 | Q) we have to modify the formula above just by replacing f by fs := Q N2 −k+1 t−2k+2−2s f1 | U (t,N )=1,t|Q∞ Q 2 ·t N2 ∗ 17 p-ADIC INTERPOLATION FOR TRIPLE L-FUNCTIONS: ANALYTIC ASPECTS where U (·)∗ denotes the adjoint of the usual U (·)-operator with respect to the Petersson product.
2, 251-292. A. Panchishkin, Non-Archimedean Mellin transform and p-adic L-functions, Vietnam J. Math. 3 (1997), 179-202. A. Panchishkin, On the Siegel-Eisenstein measure, Israel J. Math. 120, Part B (2000), 467-509. A. Panchishkin, A new method of constructing p-adic L-functions associated with modular forms, Moscow Math. J. 2 (2002), 1-16. A. Panchishkin, On p-adic integration in spaces of modular forms and its applications, J. Math. Sci. ) 115 (2003) no. 3, 2357-2377. A. Panchishkin, Two variable p-adic L-functions attached to eigenfamilies of positive slope, Invent.
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