Differential Algebraic Methods in Analytic Number Theory: A Constructive Framework for Explicit Formulae and Prime Distribution

2025 · doi:10.22541/au.176185629.96463300/v1
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Abstract

本文为解析数论建立了全面的微分代数框架，建立了L函数、模形式和素数分布的显式表示定理。我们通过精心定义的递归附加过程构建解析数论微分闭包K ANT，该过程结合了L函数可构造族的解析延续、模微分方程的解以及从零分布和泛函方程派生的组合校正项。在这个闭包中，我们证明了广泛的数论函数类别允许将特定解与谱展开相结合的显式表示。该框架通过区间算术提供经过认证的误差边界，并建立了严格的验证协议。我们开发了具有精确复杂性分析的高效算法，并展示了在素数计数、L 函数计算以及与随机矩阵理论和量子计算的连接中的应用。这项工作连接了微分代数、解析数论和计算数学，为经典问题提供了新的建设性视角，同时保持了数学的严谨性和实际可实施性。 Supplementary Material File (analytic_number_theory.pdf) - Download - 424.66 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 175views 126downloads Citations Download citation shifa liu. Differential Algebraic Methods in Analytic Number Theory: A Constructive Framework for Explicit Formulae and Prime Distribution. Authorea. 30 October 2025. DOI: https://doi.org/10.22541/au.176185629.96463300/v1 DOI: https://doi.org/10.22541/au.176185629.96463300/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