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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.


Lower bounds for Z-numbers
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by Artūras Dubickas and Michael J. Mossinghoff PDF
Math. Comp. 78 (2009), 1837-1851 Request permission


Let $p/q$ be a rational noninteger number with $p>q\geq 2$. A real number $\lambda >0$ is a $Z_{p/q}$-number if $\{\lambda (p/q)^n\}<1/q$ for every nonnegative integer $n$, where $\{x\}$ denotes the fractional part of $x$. We develop several algorithms to search for $Z_{p/q}$-numbers, and use them to determine lower bounds on such numbers for several $p$ and $q$. It is shown, for instance, that if there is a $Z_{3/2}$-number, then it is greater than $2^{57}$. We also explore some connections between these problems and some questions regarding iterated maps on integers.
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Additional Information
  • Artūras Dubickas
  • Affiliation: Department of Mathematics and Informatics, Vilnius University Naugarduko 24, LT-03225 Vilnius, Lithuania
  • Email:
  • Michael J. Mossinghoff
  • Affiliation: Department of Mathematics, Davidson College, Davidson, North Carolina 28035-6996
  • MR Author ID: 630072
  • ORCID: 0000-0002-7983-5427
  • Email:
  • Received by editor(s): January 22, 2008
  • Received by editor(s) in revised form: August 7, 2008
  • Published electronically: January 23, 2009
  • Additional Notes: The research of the first author was partially supported by the Lithuanian State Science and Studies Foundation.
  • © Copyright 2009 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 1837-1851
  • MSC (2000): Primary 11K31; Secondary 11J71, 11Y35
  • DOI:
  • MathSciNet review: 2501079