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

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736460-5

MathSciNet review:
736460

Full-text PDF Free Access

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Abstract: Let ${M_p}(\alpha )$ be the *p*th root of the mean absolute values of the *p*th 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