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Veech systems and spectral characterization of tameness with applications to Number Theory | e. H. el Abdalaoui
; M. Nerurkar
; | Date: |
15 Jan 2020 | Abstract: | We explore the notion of discrete spectrum and its various characterizations
for ergodic measure preserving actions of an amenable group on a compact metric
space. We further present a spectral characterization of tameness and we
establish that the strong Veech systems are tame. In particular, for any
amenable group $T$ the flow on the orbit closure of the translates of a ’Veech
function’ $fin mathbb{K}(T)$ is tame. As a consequence, we obtain an
improvement of Motohashi-Ramachandra 1976’s theorem on the Mertens function in
short interval, by establishing that M"{o}bius orthogonality conjecture of
Sarnak holds for those systems. | Source: | arXiv, 2001.5947 | Services: | Forum | Review | PDF | Favorites |
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