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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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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