Periods of rational maps modulo primes
2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 355, no 2, 637-660 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:kth:diva-118134DOI: 10.1007/s00208-012-0799-8ISI: 000313496700009ScopusID: 2-s2.0-84872359219OAI: oai:DiVA.org:kth-118134DiVA: diva2:604928
FunderKnut and Alice Wallenberg FoundationSwedish Research Council
QC 201302122013-02-122013-02-122013-02-14Bibliographically approved