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Periods of rational maps modulo primes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
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2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 355, no 2, 637-660 p.Article in journal (Refereed) Published
Abstract [en]

Let K be a number field, let be a rational map of degree at least 2, and let . We show that if alpha is not in the forward orbit of beta, then there is a positive proportion of primes of K such that is not in the forward orbit of . Moreover, we show that a similar result holds for several maps and several points. We also present heuristic and numerical evidence that a higher dimensional analog of this result is unlikely to be true if we replace alpha by a hypersurface, such as the ramification locus of a morphism .

Place, publisher, year, edition, pages
2013. Vol. 355, no 2, 637-660 p.
Keyword [en]
Polynomials, Orbits
National Category
URN: urn:nbn:se:kth:diva-118134DOI: 10.1007/s00208-012-0799-8ISI: 000313496700009ScopusID: 2-s2.0-84872359219OAI: diva2:604928
Knut and Alice Wallenberg FoundationSwedish Research Council

QC 20130212

Available from: 2013-02-12 Created: 2013-02-12 Last updated: 2013-02-14Bibliographically approved

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Kurlberg, Pär
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