On the error term in Weyl's law for the Heisenberg manifolds

2008/05/26 by Wenguang Zhai, Zhai, Wenguang
Mathematics · #11N37 #35P20 #58J50 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Optimization and Control (math.OC) #advanced mathematical theories #math.OC #msc:11N37 #msc:35P20 #msc:58J50

paper · pdf · doi:10.48550/arxiv.0805.3856

45 Pages

arxiv created 2008/05/26 · openalex publication_date 2008/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a fixed integer l≥ 1, let R(t) denote the error term in the Weyl's law of a (2l+1)-dimensional Heisenberg manifold with the metric g_l. In this paper we shall prove the asymptotic formula of the k-th power moment for any integers 3≤ k≤ 9. We shall also prove that the function t^-(l-1/4)R(t) has a distribution function.

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