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Wildly ramified power series with large multiplicity
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-0510-6782
2021 (English)In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 225, no August, p. 174-197Article in journal (Refereed) Published
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Abstract [en]

In this paper we consider wildly ramified power series, i.e., power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under change of coordinates called the second residue fixed point index, and provide a closed formula for it. As the name suggests this invariant is closely related to the residue fixed point index, and they coincide in the case that the power series have small multiplicity. Finally, we characterize power series with large multiplicity having the smallest possible multiplicity at the origin under iteration, in terms of this new invariant.

Place, publisher, year, edition, pages
Elsevier, 2021. Vol. 225, no August, p. 174-197
Keywords [en]
Non-archimedean dynamics, Lower ramification numbers, Formal classification of power series in positive characteristic
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-93053DOI: 10.1016/j.jnt.2021.01.019ISI: 000651605300007Scopus ID: 2-s2.0-85102576781Local ID: 2021OAI: oai:DiVA.org:lnu-93053DiVA, id: diva2:1416205
Available from: 2020-03-22 Created: 2020-03-22 Last updated: 2021-06-11Bibliographically approved

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Nordqvist, Jonas

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