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Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers. (English) Zbl 0852.11058
The author uses semi-linear programming to find the fifth and sixth smallest values of the absolute Mahler measure for totally positive algebraic integers (the first four have been determined by C. J. Smyth [Math. Comput. 37, 205-208 (1981; Zbl 0475.12001)]).

MSC:
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11J68 Approximation to algebraic numbers
11R04 Algebraic numbers; rings of algebraic integers
11Y40 Algebraic number theory computations
90C34 Semi-infinite programming
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References:
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[2] V. Flammang, Sur la longueur des entiers algébriques totalement positifs, J. Number Theory (to appear). · Zbl 0831.11057
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[4] C. J. Smyth, On the measure of totally real algebraic integers, J. Austral. Math. Soc. Ser. A 30 (1980/81), no. 2, 137 – 149. C. J. Smyth, On the measure of totally real algebraic integers. II, Math. Comp. 37 (1981), no. 155, 205 – 208. · Zbl 0457.12001
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