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Full-Text Articles in Physical Sciences and Mathematics
Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech
Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech
Paul Gunnells
We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycle introduced by R. Sczech. Hence we obtain a polynomial time algorithm for computing these special values. Second, we show how to use our techniques to compute certain special values of the Witten zeta function, and we compute some …
Hecke Operators And Q-Groups Associated To Self-Adjoint Homogeneous Cones, Pe Gunnells, M Mcconnell
Hecke Operators And Q-Groups Associated To Self-Adjoint Homogeneous Cones, Pe Gunnells, M Mcconnell
Paul Gunnells
Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over , and let ΓG be an appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph (Invent. Math. 55 (1979) 241) to a larger class of groups, and proposes techniques to compute the Hecke-module structure of previously inaccessible cohomology groups.