Arithmetic Algebraic Closure: A Rigorous Framework for Explicit Representations in Number Theory

2025 · doi:10.22541/au.176185632.28832898/v1
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Abstract

本文通过构建算术代数闭包，为数论中的显式表示建立了一个全面的框架。在微分代数的基础工作和微分代数闭包的最新进展的基础上，我们将这种方法扩展到具有完全数学严谨性的算术数论。我们提供了算术导数算子的详细构造，推导了带有组合校正项的代数数的显式公式，开发了具有复杂性分析的完整算法，并展示了广泛的数值验证。该框架保持与经典不可能结果的一致性，同时为计算数论应用提供了前所未有的准确性。我们的工作揭示了数论、组合学和微分代数之间的深刻联系，为丰富数学结构中的显式可解性提供了新的视角。主要创新包括：对通用域扩展的算术导数进行严格定义;用于算术代数闭包的构造塔;与 zeta 值有已证明的联系的组合系数;具有保证精度的显式解公式;并通过微分伽罗瓦理论与阿贝尔-鲁菲尼定理完全调和。 Supplementary Material File (arithmitic_number_theory.pdf) - Download - 434.33 KB Information & Authors Information Version history Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

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Authors Metrics & Citations Metrics Article Usage 290views 135downloads Citations Download citation Dongqi Liu, shifa liu. Arithmetic Algebraic Closure: A Rigorous Framework for Explicit Representations in Number Theory. Authorea. 30 October 2025. DOI: https://doi.org/10.22541/au.176185632.28832898/v1 DOI: https://doi.org/10.22541/au.176185632.28832898/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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last seen: 2026-05-20T01:45:00.602351+00:00