Two-Dimensional Analogs of the Minkowski ?(x) Function
Andrew Marder
Abstract
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.
Create a lesson
Related papers
Conguences for Odd Unimodal Sequences and a Problem of Bringmann And Lovejoy
Koustav Banerjee, Manosij Ghosh Dastidar
Primes between 8th powers?
Matt Visser
Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve
SeungJu Lee
On the Erdős--Odlyzko--Sárközy conjecture for prime-power moduli
William Banks, Igor E. Shparlinski
The Density and Quantitative Upper Bound of Integers Not Expressible as the Sum of a Prime and a Zumkeller Number
Ting Hon Stanford Li
On a problem on partitions into distinct primes
John M. Campbell