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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Generating random factored Gaussian integers, easily
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by Noah Lebowitz-Lockard and Carl Pomerance PDF
Math. Comp. 85 (2016), 503-516 Request permission

Abstract:

We present a (random) polynomial-time algorithm to generate a random Gaussian integer with the uniform distribution among those with norm at most $N$, along with its prime factorization. The method generalizes to finding a random ideal in the ring of integers of a quadratic number field together with its prime ideal factorization. We also discuss the analogous problem for higher degree number fields.
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Additional Information
  • Noah Lebowitz-Lockard
  • Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30307
  • MR Author ID: 1128605
  • Email: nlebowi@emory.edu
  • Carl Pomerance
  • Affiliation: Mathematics Department, Dartmouth College, Hanover, New Hampshire 03755
  • MR Author ID: 140915
  • Email: carl.pomerance@dartmouth.edu
  • Received by editor(s): July 19, 2013
  • Received by editor(s) in revised form: April 22, 2014
  • Published electronically: June 23, 2015
  • Additional Notes: This paper is based on the 2013 senior thesis of the first author written under the direction of the second author at Dartmouth College. The second author was supported in part by NSF grant DMS-1001180.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 503-516
  • MSC (2010): Primary 11416; Secondary 65C10, 11K45
  • DOI: https://doi.org/10.1090/mcom/3000
  • MathSciNet review: 3404459