Torsions in Cohomology of SL₂(ℤ) and Congruence of Modular Forms

2019/05/13 by Deng, Taiwang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.05260

Abstract

We describe torsion classes in the first cohomology group of SL₂(ℤ). In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology group of SL₂(ℤ) as a module over the torsion invariants. As application, we obtain various congruences between cuspidal forms of level one and Eisenstein series.

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