TY - JOUR
T1 - Cohomology of congruence subgroups of SL (4, Z) II
AU - Ash, Avner
AU - Gunnells, Paul E.
AU - McConnell, Mark
N1 - Funding Information:
The first author wishes to thank the National Science Foundation for support of this research through NSF grants numbers DMS-0139287 and DMS-0455240. The second author wishes to thank the National Science Foundation for support of this research through NSF grants numbers DMS-0245580 and DMS-0401525. We thank the Mathematics Departments of Columbia University and the University of Massachusetts, Amherst, for computers used to perform these computations. We also thank Armand Brumer, Dinakar Ramakrishnan, and Uwe Weselmann for helpful conversations.
PY - 2008/8
Y1 - 2008/8
N2 - In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212] we computed cohomology groups H5 (Γ0 (N), C), where Γ0 (N) is a certain congruence subgroup of SL (4, Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL (4) concretely constructed in terms of Betti cohomology.
AB - In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212] we computed cohomology groups H5 (Γ0 (N), C), where Γ0 (N) is a certain congruence subgroup of SL (4, Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL (4) concretely constructed in terms of Betti cohomology.
KW - Automorphic forms
KW - Cohomology of arithmetic groups
KW - Eisenstein cohomology
KW - Hecke operators
KW - Siegel modular forms
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U2 - 10.1016/j.jnt.2007.09.002
DO - 10.1016/j.jnt.2007.09.002
M3 - Article
AN - SCOPUS:44949149332
SN - 0022-314X
VL - 128
SP - 2263
EP - 2274
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 8
ER -