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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The parallelized Pollard kangaroo method in real quadratic function fields
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by Andreas Stein and Edlyn Teske PDF
Math. Comp. 71 (2002), 793-814 Request permission

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
  • Received by editor(s): July 10, 2000
  • Published electronically: October 4, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Math. Comp. 71 (2002), 793-814
  • MSC (2000): Primary 11Y16, 11Y40, 11R29; Secondary 11R58, 14H05
  • DOI: https://doi.org/10.1090/S0025-5718-01-01343-6
  • MathSciNet review: 1885629