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

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the *p*th root of the mean absolute values of the *p*th powers of a totally real algebraic integer . For each fixed we study the set of such . 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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C. J. Smyth,*On the measure of totally real algebraic integers. II*, Math. Comp.**37**(1981), no. 155, 205–208. MR**616373**, https://doi.org/10.1090/S0025-5718-1981-0616373-7**[15]**C. J. Smyth,*On the measure of totally real algebraic integers*, J. Austral. Math. Soc. Ser. A**30**(1980/81), no. 2, 137–149. MR**607924**

C. J. Smyth,*On the measure of totally real algebraic integers. II*, Math. Comp.**37**(1981), no. 155, 205–208. MR**616373**, https://doi.org/10.1090/S0025-5718-1981-0616373-7

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

Article copyright:
© Copyright 1984
American Mathematical Society