Weakly Commensurable Arithmetic Groups , Lengths of Closed Geodesics and Isospectral Locally Symmetric Spaces

  title={Weakly Commensurable Arithmetic Groups , Lengths of Closed Geodesics and Isospectral Locally Symmetric Spaces},
  • Published 2008
The goal of this paper is two-fold. First, we introduce and analyze a new relationship between (Zariski-dense) abstract subgroups of the group of F rational points of a connected semi-simple algebraic group defined over a field F , which we call weak commensurability. This relationship is expressed in terms of the eigenvalues of individual elements, and does not involve any structural connections between the subgroups. Nevertheless, it turns out that weakly commensurable S-arithmetic subgroups… CONTINUE READING

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