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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The parallelized Pollard kangaroo method in real quadratic function fields


Authors: Andreas Stein and Edlyn Teske
Journal: Math. Comp. 71 (2002), 793-814
MSC (2000): Primary 11Y16, 11Y40, 11R29; Secondary 11R58, 14H05
Published electronically: October 4, 2001
MathSciNet review: 1885629
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Abstract: We show how to use the parallelized kangaroo method for computing invariants in real quadratic function fields. Specifically, we show how to apply the kangaroo method to the infrastructure in these fields. We also show how to speed up the computation by using heuristics on the distribution of the divisor class number, and by using the relatively inexpensive baby steps in the real quadratic model of a hyperelliptic function field. Furthermore, we provide examples for regulators and class numbers of hyperelliptic function fields of genus $3$ that are larger than those ever reported before.


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Additional Information

Andreas Stein
Affiliation: University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 West Green Street, Urbana, Illinois 61801
Email: andreas@math.uiuc.edu

Edlyn Teske
Affiliation: University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1
Email: eteske@cacr.math.uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01343-6
PII: S 0025-5718(01)01343-6
Received by editor(s): July 10, 2000
Published electronically: October 4, 2001
Article copyright: © Copyright 2001 American Mathematical Society