Counting cosets of unimodular groups over Dedekind domains

Details Counting cosets of unimodular groups over Dedekind domains Counting cosets of unimodular groups over Dedekind domains

2011-01-19

arxiv.org/abs/1101.3683v1

Mathematics

Number Theory

14 pages

Scientific paper

In this paper, a formula for the calculation of the number of right cosets contained in a double coset with respect to a unimodular group over a Dedekind domain is developed, and applications of this formula in the theory of congruence subgroups -- an index formula -- and the theory of abstract Hecke algebras -- a reduction theorem and an algorithm for the explicit calculation of products -- are given.

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