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TitleEquidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds
Author(s)Flaminio, Livio
Cosentino, Salvatore
Heisenberg group
Cohomological equation
Issue dateNov-2015
PublisherAmerican Institute of Mathematical Sciences (AIMS)
JournalJournal of Modern Dynamics
Abstract(s)We prove quantitative equidistribution results for actions of Abelian subgroups of the (2g + 1)-dimensional Heisenberg group acting on compact (2g + 1)-dimensional homogeneous nilmanifolds. The results are based on the study of the C∞-cohomology of the action of such groups, on tame estimates of the associated cohomological equations and on a renormalization method initially applied by Forni to surface flows and by Forni and the second author to other parabolic flows. As an application we obtain bounds for finite Theta sums defined by real quadratic forms in g variables, generalizing the classical results of Hardy and Littlewood [25, 26] and the optimal result of Fiedler, Jurkat, and Körner [17] to higher dimension.
Description2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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