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The integer transfinite diameter of intervals and totally real algebraic integers

V. Flammang, G. Rhin, C. J. Smyth (1997)

Journal de théorie des nombres de Bordeaux

In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals [ r s , r s + δ ] , where r s is a fixed rational and δ 0 . We also study functions g - , g , g + associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call critical polynomials, associated to a given interval I . We show how to estimate from below the proportion of roots of an integer polynomial which is sufficiently...

Totally positive algebraic integers of small trace

Chistopher J. Smyth (1984)

Annales de l'institut Fourier

Let α be a totally positive algebraic integer, with the difference between its trace and its degree at most 6. We describe an algorithm for finding all such α , and display the resulting list of 1314 values of α which the algorithm produces.

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