代数数指数线性形式的显界

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2021-12-09 DOI:10.1145/3476446.3536170

Cheng-Chao Huang

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引用次数: 0

摘要

本文研究了λ=β1e - α1+…βmeαm，其中α_i和β_i为代数数。利用代数计算中的构造方法，从“Lindemann—Weierstrass有效定理”出发，证明了λ绝对值的显式下界。此外，利用代数数计数的结果，证明了λ有显上界的存在性。

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Explicit Bounds for Linear Forms in the Exponentials of Algebraic Numbers

In this paper, we study linear forms λ=β1eα1+...βmeαm, 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 "theoreme me 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.

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Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

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