在数字字段上进行几何选,以获得更高的时刻
Giacomo Micheli1, Severin Schraven2, Simran Tinani3
1Department of Mathematics, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620 USA.
概括
本研究介绍了一种有效的几何,用于计算数字场内的子集密度的较高时刻. 该方法计算了爱因斯坦多项式的密度,平均值和方差,扩展了之前的研究.
科学领域:
- 数学理论 数学理论
- 代数几何几何学的几何学
背景情况:
- 几何是一种计算子集密度的工具.
- 现有的方法仅限于特定的数字字段或较低的时刻.
研究的目的:
- 开发一种有效的标准,用于计算在一般数字场上较高密度的时刻.
- 为了将密度计算的几何扩展到代数整数环和更高的时刻.
主要方法:
- 一个通用的几何被开发用于计算密度的更高时刻.
- 该方法应用于数域中的代数整数上的有限维自由模块.
主要成果:
- 建立了一个有效的标准来计算所有更高密度的时刻.
- 几何被扩展到一般的数场和更高的时刻,超越了以前的限制.
结论:
- 开发的几何提供了一种统一且有效的密度时刻计算方法.
- 这项工作将对数论应用的几何的现有结果进行概括和增强.
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