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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 2024 MCQ for Mathematics of Computation is 1.78.

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The mean values of totally real algebraic integers
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by C. J. Smyth PDF
Math. Comp. 42 (1984), 663-681 Request permission

Abstract:

Let ${M_p}(\alpha )$ be the pth root of the mean absolute values of the pth powers of a totally real algebraic integer $\alpha$. For each fixed $p > 0$ we study the set ${\mathfrak {M}_p}$ of such ${M_p}(\alpha )$. We show that its structure is as follows: on the nonnegative real line it consists of some isolated points, followed by a small interval in which its structure is as yet undetermined. Beyond this small interval, it is everywhere dense.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 663-681
  • MSC: Primary 11R80; Secondary 11R04, 11S05
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0736460-5
  • MathSciNet review: 736460