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Mathematics of Computation

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The mean values of totally real algebraic integers

Author: C. J. Smyth
Journal: Math. Comp. 42 (1984), 663-681
MSC: Primary 11R80; Secondary 11R04, 11S05
MathSciNet review: 736460
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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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Article copyright: © Copyright 1984 American Mathematical Society