On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties

1995 ◽  
Vol 7 (7) ◽  
pp. 1-28 ◽  
Author(s):  
Joachim Schwermer
Keyword(s):  
Eisenstein Cohomology ◽  
Euler Products ◽  
Modular Varieties

ON SIEGEL MODULAR VARIETIES OF LEVEL 3

1991 ◽  
Vol 02 (01) ◽  
pp. 17-35 ◽  
Author(s):  
TOMOYOSHI IBUKIYAMA
Keyword(s):  
Level 3 ◽  
Modular Varieties

scholarly journals Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)

2009 ◽  
Vol 146 (1) ◽  
pp. 21-57 ◽  
Author(s):  
Harald Grobner
Keyword(s):  
Algebraic Group ◽  
Eisenstein Series ◽  
Symplectic Group ◽  
Automorphic Forms ◽  
General Theorem ◽  
Simple Algebraic Group ◽  
Ramanujan Conjecture ◽  
Eisenstein Cohomology ◽  
Derivatives Of

AbstractLetGbe the simple algebraic group Sp(2,2), to be defined over ℚ. It is a non-quasi-split, ℚ-rank-two inner form of the split symplectic group Sp8of rank four. The cohomology of the space of automorphic forms onGhas a natural subspace, which is spanned by classes represented by residues and derivatives of cuspidal Eisenstein series. It is called Eisenstein cohomology. In this paper we give a detailed description of the Eisenstein cohomologyHqEis(G,E) ofGin the case of regular coefficientsE. It is spanned only by holomorphic Eisenstein series. For non-regular coefficientsEwe really have to detect the poles of our Eisenstein series. SinceGis not quasi-split, we are out of the scope of the so-called ‘Langlands–Shahidi method’ (cf. F. Shahidi,On certainL-functions, Amer. J. Math.103(1981), 297–355; F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certainL-functions, Ann. of Math. (2)127(1988), 547–584). We apply recent results of Grbac in order to find the double poles of Eisenstein series attached to the minimal parabolicP0ofG. Having collected this information, we determine the square-integrable Eisenstein cohomology supported byP0with respect to arbitrary coefficients and prove a vanishing result. This will exemplify a general theorem we prove in this paper on the distribution of maximally residual Eisenstein cohomology classes.

Effective Estimates for the Distribution of Values of Euler Products

2005 ◽  
Vol 145 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Ernesto Girondo ◽  
Jörn Steuding
Keyword(s):  
Distribution Of Values ◽  
Euler Products

scholarly journals COHERENT SYSTEMS AND MODULAR SUBAVRIETIES OF $\mathcal{SU}_C(r)$

2012 ◽  
Vol 23 (04) ◽  
pp. 1250037 ◽  
Author(s):  
MICHELE BOLOGNESI ◽  
SONIA BRIVIO
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Low Rank ◽  
Coherent Systems ◽  
Projective Varieties ◽  
Complex Curve ◽  
Smooth Complex ◽  
Moduli Theory ◽  
Modular Varieties ◽  
Small Genus

Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙr-1)rg// PGL (r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces.

Analytic behavior of some Euler products

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Jinho Han ◽  
Haseo Ki ◽  
Donghoon Park
Keyword(s):  
Analytic Behavior ◽  
Euler Products
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