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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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Computing totally positive algebraic integers of small trace
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by James McKee PDF
Math. Comp. 80 (2011), 1041-1052 Request permission

Abstract:

We construct minimal polynomials of totally positive algebraic integers of small absolute trace by consideration of their reductions modulo auxiliary polynomials. Many new examples of such polynomials of minimal absolute trace (for given degree) are found. The computations are pushed to degrees that previously were unattainable, and one consequence is that the new examples form the majority of all those known. As an application, we produce a new bound for the Schur-Siegel-Smyth trace problem.
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Additional Information
  • James McKee
  • Affiliation: Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, England, United Kingdom
  • Email: james.mckee@rhul.ac.uk
  • Received by editor(s): December 23, 2009
  • Received by editor(s) in revised form: February 22, 2010
  • Published electronically: October 22, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1041-1052
  • MSC (2010): Primary 11R04, 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02424-X
  • MathSciNet review: 2772109