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The isotropic lines of Z_{d}^{2}

Abstract : We show that the isotropic lines in the lattice Z_{d}^{2} are the Lagrangian submodules of that lattice and we give their number together with the number of them through a given point of the lattice. The set of isotropic lines decompose into orbits under the action of SL(2,Z_d). We give an explicit description of those orbits as well as their number and their respective cardinalities. We also develop two group actions on the group \Sigma_{D}(M) related to the topic.
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Preprints, Working Papers, ...
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Contributor : Olivier Albouy <>
Submitted on : Thursday, September 18, 2008 - 2:43:43 PM
Last modification on : Tuesday, October 29, 2019 - 4:04:08 PM
Long-term archiving on: : Friday, June 4, 2010 - 11:33:11 AM


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  • HAL Id : in2p3-00322707, version 1
  • ARXIV : 0809.3220


Olivier Albouy. The isotropic lines of Z_{d}^{2}. 2008. ⟨in2p3-00322707v1⟩



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