Cohomology of congruence subgroups of SL4(ℤ). III

Avner Ash, Paul E. Gunnells, Mark McConnell

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Abstract

In two previous papers we computed cohomology groups H50(N); ℂ) for a range of levels N, where Γ0(N) is the congruence subgroup of SL4(ℤ) consisting of all matrices with bottom row congruent to (0, 0, 0, *) mod N. In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main focus of the paper. Our computations involve matrices with up to 20 million nonzero entries. We also make two conjectures concerning the contributions to H50(N); [ℂ]) for N prime coming from Eisenstein series and Siegel modular forms.

Original languageEnglish (US)
Pages (from-to)1811-1831
Number of pages21
JournalMathematics of Computation
Volume79
Issue number271
DOIs
StatePublished - Jul 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Automorphic forms
  • Cohomology of arithmetic groups
  • Eisenstein cohomology
  • Hecke operators
  • Paramodular group
  • Siegel modular forms
  • Smith normal form
  • Sparse matrices

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