2004/05/24 by Andrew Marder, Marder, Andrew · 1 citation
Mathematics · Physics and Astronomy · #11J70 #11K50 #26A30 #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #math.CA #math.NT #msc:11J70 #msc:11K50 #msc:26A30
paper · pdf · doi:10.48550/arxiv.math/0405446
50 pages, 13 figures, for associated applet, see http://wso.williams.edu/~amarder/applets/
arxiv created 2004/05/24 · openalex publication_date 2004/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two generalizations of the Minkowski ?(x) function are given. As ?(x) maps quadratic irrationals to rational numbers, it is shown that both generalizations send natural classes of pairs of cubic irrational numbers in the same cubic number field to pairs of rational numbers. It is also shown that these functions satisfy an analog to the fact that ?(x), while continuous and increasing, has derivative zero almost everywhere. Both extend earlier work of Beaver-Garrity on the Farey-Bary map.