Power series in P-adic roots of unity

Simple item page
dc.contributor.advisorVoloch, Jose Felipeen
dc.creatorNeira, Ana Raissa Bernardoen
dc.date.accessioned2008-08-28T21:35:38Zen
dc.date.accessioned2017-05-11T22:15:57Z
dc.date.available2008-08-28T21:35:38Zen
dc.date.available2017-05-11T22:15:57Z
dc.date.issued2002en
dc.descriptiontexten
dc.description.abstractMotivated by [5], we develop an analogy with a similar problem in p-adic power series over a finite field extension of Qp, say K. Concerned with the convergence of the p-adic power series, we naturally assume that it converges in the unit disc, since we calculate the values of this power series at roots of unity in Q¯ p. This dissertation is devoted to the proof of the following result. Let F(x1,...,xn) be a power series over K, a finite field extension of Qp, converging in On K = {(x1,...,xn) ∈ Kn| max 1≤i≤n {|xi|p} ≤ 1}. Then, there exists a positive constant c such that for any roots of unity ζ1,...,ζn in the algebraic closure of Qp either F(ζ1,...,ζn) = 0 or |F(ζ1,...,ζn)|p ≥ c. We also compute some constants c associated to certain power series as illustrations of the result. In these examples, we realize that the constant c is not unique nor does it follow a pattern. Unfortunately, it’s not known any general formula for c.
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifierb57170174en
dc.identifier.oclc56826913en
dc.identifier.proqst3110664en
dc.identifier.urihttp://hdl.handle.net/2152/811en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshPower seriesen
dc.subject.lcshp-adic numbersen
dc.titlePower series in P-adic roots of unityen
dc.type.genreThesisen

Files

Collections

University of Texas at Austin