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Wreath Products and Proportions of Periodic Points
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 13, 3944-3969 p.Article in journal (Refereed) Published
Abstract [en]

Let phi : P-1 -> P-1 be a rational map of degree greater than 1 defined over a number field k with ring of integers o(k). For each prime p of good reduction for phi, we let phi(p) denote the reduction of phi modulo p. A random map heuristic suggests that for large p, the proportion of periodic points of phi(p) in P-1 (o(k)/p) should be small. We show that this is indeed the case for many rational functions phi.

Place, publisher, year, edition, pages
Oxford University Press, 2016. no 13, 3944-3969 p.
Keyword [en]
Density, Polynomials
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URN: urn:nbn:se:kth:diva-194051DOI: 10.1093/imrn/rnv273ISI: 000383777700005ScopusID: 2-s2.0-84981313734OAI: diva2:1037538

QC 20161017

Available from: 2016-10-17 Created: 2016-10-14 Last updated: 2016-10-17Bibliographically approved

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Kurlberg, Pär
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