Explicit Bounds for Linear Forms in the Exponentials of Algebraic Numbers

12/09/2021

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by   Cheng-Chao Huang, et al.

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In this paper, we study linear forms λ = β_1e^α_1+⋯+β_me^α_m, where α_i and β_i are algebraic numbers. An explicit lower bound for the absolute value of λ is proved, which is derived from "théorème de Lindemann–Weierstrass effectif" via constructive methods in algebraic computation. Besides, the existence of λ with an explicit upper bound is established on the result of counting algebraic numbers.