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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.

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.


A log-log speedup for exponent one-fifth deterministic integer factorisation
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by David Harvey and Markus Hittmeir HTML | PDF
Math. Comp. 91 (2022), 1367-1379 Request permission


Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer $N$ may be rigorously and deterministically factored into primes in at most \[ O\left ( \frac {N^{1/5} \log ^{16/5} N}{(\log \log N)^{3/5}}\right ) \] bit operations. This improves on the previous best known result by a factor of $(\log \log N)^{3/5}$.
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Additional Information
  • David Harvey
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
  • MR Author ID: 734771
  • ORCID: 0000-0002-4933-658X
  • Email:
  • Markus Hittmeir
  • Affiliation: SBA Research, Floragasse 7, A-1040 Vienna, Austria
  • MR Author ID: 1220564
  • ORCID: 0000-0002-3363-6270
  • Email:
  • Received by editor(s): June 8, 2021
  • Received by editor(s) in revised form: October 12, 2021
  • Published electronically: December 15, 2021
  • Additional Notes: Dedicated to Richard Brent on the occasion of his $(3 \times 5^2)$-th birthday
    The first author was supported by the Australian Research Council (grant FT160100219).
    SBA Research (SBA-K1) is a COMET Centre within the framework of COMET – Competence Centers for Excellent Technologies Programme and funded by BMK, BMDW, and the federal state of Vienna. The COMET Programme is managed by FFG
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 1367-1379
  • MSC (2020): Primary 11Y05
  • DOI:
  • MathSciNet review: 4405498