Details:
Title  Regular and residual Eisenstein series and the automorphic cohomology of $textSp(2,2)$.  Author(s)  Harald Grobner  Type  Article in Journal  Abstract  Let G be the simple algebraic group Sp(2,2), to be defined over xs211A. It is a nonquasisplit, xs211Aranktwo inner form of the split symplectic group Sp8 of rank four. The cohomology of the space of automorphic forms on G has 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 cohomology HqEis(G,E) of G in the case of regular coefficients E. It is spanned only by holomorphic Eisenstein series. For nonregular coefficients E we really have to detect the poles of our Eisenstein series. Since G is not quasisplit, we are out of the scope of the socalled ‘Langlands–Shahidi method’ (cf. F. Shahidi, On certain Lfunctions, Amer. J. Math. 103 (1981), 297–355; F. Shahidi, On the Ramanujan conjecture and finiteness of poles for certain Lfunctions, 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 parabolic P0 of G. Having collected this information, we determine the squareintegrable Eisenstein cohomology supported by P0 with 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.  Keywords  cohomology of arithmetic groups; Eisenstein cohomology; cuspidal automorphic representation; Eisenstein series; residual spectrum  ISSN  0010437X; 15705846/e 
URL 
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7089216&fileId=S0010437X09004266 
Language  English  Journal  Compos. Math.  Volume  146  Number  1  Pages  2157  Publisher  Cambridge University Press, Cambridge; London Mathematical Society, London  Year  2010  Edition  0  Translation 
No  Refereed 
No 
