Irrationality Measures, Irrationality Bases, and a Theorem of Jarnik

Simple item page
dc.creatorSondow, Jonathan
dc.date2004-06-15
dc.date.accessioned2026-07-07T05:09:15Z
dc.date.available2026-07-07T05:09:15Z
dc.descriptionIn math.NT/0307308 we defined the irrationality base of an irrational number and, assuming a stronger hypothesis than the irrationality of Euler's constant, gave a conditional upper bound on its irrationality base. Here we develop the general theory of the irrationality exponent and base, giving formulas and bounds for them using continued fractions and the Fibonacci sequence. A theorem of Jarnik on Diophantine approximation yields numbers with prescribed irrationality measure. By another method we explicitly construct series with prescribed irrationality base. Many examples are given.
dc.description14 pages, presented in part at Journeés Arithmetiques XXIII in Graz
dc.identifierhttps://arxiv.org/abs/math/0406300
dc.identifierhttp://arxiv.org/abs/math/0406300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71562
dc.subjectNumber Theory
dc.subject11J82
dc.titleIrrationality Measures, Irrationality Bases, and a Theorem of Jarnik
dc.typetext

Files

Collections

arXiv