The mean values of totally real algebraic integers

Smyth, C. J.

doi:10.1090/S0025-5718-1984-0736460-5

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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