By David Ginzburg, Erez Lapid, David Soudry
This booklet is the second one of 2 volumes, which characterize best subject matters of present study in automorphic kinds and illustration conception of reductive teams over neighborhood fields. Articles during this quantity customarily symbolize international elements of automorphic varieties. one of the themes are the hint formulation; functoriality; representations of reductive teams over neighborhood fields; the relative hint formulation and sessions of automorphic varieties; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions. The articles are written via top researchers within the box, and convey the reader, complicated graduate scholars and researchers alike, to the frontline of the energetic examine in those deep, very important issues. The spouse quantity (""Contemporary arithmetic, quantity 488"") is dedicated to international facets of automorphic kinds
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Extra info for Automorphic Forms and L-functions II: Local Aspects
We use tacitly that only 1 , 2 which are coprime to N may appear. We then rephrase the summations over 1 , 2 and v2 in terms of r. We observe that r ≡ −v1 C 1 mod N 2 gives after multiplication by B t (observing B t C ≡ −12 mod N ) v¯1 B t r ≡ 1 mod N, 2 and hence (using an obvious notation: multiplication of a row of characters with a column of arguments) 1 (χ1 , χ2 ) 2 = χ1 (v¯1 )χ2 (v¯1 )(χ1 , χ2 )(B t · r). In the next step, we write r=t·s Then we have to sum over with t = gcd(r1 , r2 ). ¨ SIEGFRIED BOCHERER AND ALEXEI A.
Providence, RI, 2000. J. Sturm, The critical values of zeta functions associated to the symplectic group, Duke Math. J. 48 (1981), 327-350. M. Visik, Non-Archimedean measures connected with Dirichlet series, Math. USSR Sb. 28 (1976), 216-228. 74, F-38402 St.
Deligne, Valeurs de fonctions L et p´ eriodes d’int´ egrales, Proc. Symp. , Amer. Math. Soc. 33 (part 2) (1979), 313-342. [Fei86] P. Feit, Poles and Residues of Eisenstein Series for Symplectic and Unitary Groups, Memoir Amer. Math. Soc. 61 (1986), no. 346. [Am-V] 38 [Fr] ¨ SIEGFRIED BOCHERER AND ALEXEI A. PANCHISHKIN E. Freitag, Siegelsche Modulfunktionen Grundlehren der mathematischen Wissenschaften 254, Springer, 1981. B. Garrett, Integral representations of certain L-functions attached to one, two and three modular forms, University of Minnesota Technical Reports 131-86 (1986).
Automorphic Forms and L-functions II: Local Aspects by David Ginzburg, Erez Lapid, David Soudry