2010/01/22 by Felix Fontein, Fontein, Felix, Eric Landquist +3
Computer Science · Mathematics · #11M38 #11R29 #11R58 #11R65 #11Y16 #11Y40 #14H05 #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11M38 #msc:11R29 #msc:11R58 #msc:11R65 #msc:11Y16 #msc:11Y40 #msc:14H05
paper · pdf · doi:10.48550/arxiv.1001.4095
14 pages, 3 figures
arxiv created 2010/01/22 · openalex publication_date 2010/01/22 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe and give computational results of a procedure to compute the divisor class number and regulator of most purely cubic function fields of unit rank 2. Our implementation is an improvement to Pollard's Kangaroo method in infrastructures, using distribution results of class numbers as well as information on the congruence class of the divisor class number, and an adaptation that efficiently navigates these torus-shaped infrastructures. Moreover, this is the first time that an efficient "square-root" algorithm has been applied to the infrastructure of a global field of unit rank 2. With the exception of certain function fields defined by Picard curves, our examples are the largest known divisor class numbers and regulators ever computed for a function field of genus 3.