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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.


Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8
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by V. Flammang HTML | PDF
Math. Comp. 90 (2021), 379-388 Request permission


Previously, we established lower bounds for the usual measures (trace, length, Mahler measure) of totally positive algebraic integers, i.e., all of whose conjugates are positive real numbers. We used the method of explicit auxiliary functions and we noticed that the house of most of the totally positive polynomials involved in our functions are bounded by 5.8. Thanks to this observation, we are able to use the same method and give upper bounds for the usual measures of totally positive algebraic integers with house bounded by this value. To our knowledge, theses upper bounds are the first results of this kind.
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Additional Information
  • V. Flammang
  • Affiliation: UMR CNRS 7502, IECL, Université de Lorraine, site de Metz, Département de Mathématiques, UFR MIM, 3 rue Augustin Fresnel BP 45112 57073 Metz cedex 3 France
  • MR Author ID: 360354
  • Email:
  • Received by editor(s): April 21, 2020
  • Published electronically: September 8, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 379-388
  • MSC (2010): Primary 11C08, 11R06, 11Y40
  • DOI:
  • MathSciNet review: 4166465