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Article Dans Une Revue Rocky Mountain Journal of Mathematics Année : 2020

The S-measure for algebraic integers having all their conjugates in a sector

Valérie Flammang
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Résumé

Let α be a nonzero algebraic integer of degree d whose all conjugates α 1 = α, α 2 ,. .. , α d lie in a sector | arg z| ≤ θ, 0 < θ ≤ 90 •. We define the S-measure of α by S(α) = d i=1 |α i | and the absolute S-measure of α by s(α) = S(α)/d. We compute the greatest lower bound c(θ) of s(α) for α belonging to twelve subintervals of (0, θ). Among these subintervals, three are complete. These computations use the principle of explicit auxiliary functions and our recursive algorithm.
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Dates et versions

hal-03295906 , version 1 (22-07-2021)

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Valérie Flammang. The S-measure for algebraic integers having all their conjugates in a sector. Rocky Mountain Journal of Mathematics, 2020, 50 (4), pp.1313-1321. ⟨10.1216/rmj.2020.50.1313⟩. ⟨hal-03295906⟩
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