lattice theory and toeplitz determinants albrecht b ottcher lenny fukshansky stephan ramon garcia and hiren maharaj abstract this is a survey of our recent joint investigations of lattices that are ...
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...Lattice theory and toeplitz determinants albrecht b ottcher lenny fukshansky stephan ramon garcia hiren maharaj abstract this is a survey of our recent joint investigations lattices that are generated by nite abelian groups in the case cyclic volume fundamental domain such perturbed determinant with simple fisher hartwig symbol for general situation more complicated but it can still be tackled pure matrix main result on under consideration states they always have basis minimal vectors while results other direction concern exact asymptotic formulas slightly modied version talk given rst author at humboldt kolleg iwota tbilisi mainly operator theorists therefore also contains an introduction to basics msc primary h secondary c keywords packing group determi nant n analogue acknowledges support simons foundation grant nsa nsf dms deta whereas t equals dett notation means emerge problem formula detan was established onlyin dettn special cases well known one encounters statistical physics m...