Lower Bounds on the Dimension of the Cohomology of Bianchi Groups via Sczech Cocyles
Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 1, pp. 237-260.

Using Sczech cocyles, we compute the traces of certain involutions on the Eisenstein cohomology of principal congruence subgroups of Bianchi groups. These traces, combined with results of [13, 14, 2], give explicit lower bounds for the cuspidal cohomology of these groups. The asymptotic lower bounds that follow from our results complement the recent asymptotic upper bounds found in [4, 5, 12].

En utilisant les cocyles de Sczech, nous calculons les traces de certaines involutions sur la cohomologie d’Eisenstein pour les sous-groupes de congruence principaux de groupes de Bianchi. Ces traces, combinées avec les résultats de [13, 14, 2], donnent des bornes inférieures explicites pour la cohomologie cuspidale de ces groupes. Les bornes asymptotiques inférieures qui découlent de nos résultats complètent les bornes asymptotiques supérieures récemment obtenues dans [4, 5, 12].

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.937
Classification: 11F75
Keywords: Bianchi groups, Bianchi modular forms, Lefschetz numbers
Mehmet Haluk Şengün 1; Seyfi Türkelli 2

1 School of Mathematics and Statistics University of Sheffield Hicks Building, Hounsfield Road Sheffield S3 7RH UK
2 476 Morgan Hall, 1 University Circle Department of Mathematics Western Illinois University Macomb, IL 61455 USA
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Mehmet Haluk Şengün; Seyfi Türkelli. Lower Bounds on the Dimension of the Cohomology of Bianchi Groups via Sczech Cocyles. Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 1, pp. 237-260. doi : 10.5802/jtnb.937. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.937/

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