论文标题
El Googaritmo积分：NúmerosPrimosyAlgoMás
El Logaritmo Integral: Números primos y algo más
论文作者
论文摘要
我们展示了对数积分功能在19世纪上半叶数学发展中的相关性。它的重要性涉及一级数学家，例如Euler，Gauss，Bessel，Riemann。我们的观点是对原始资源进行详细研究的结果。我们设法建立了进步的时间表。特别是，我们的研究证明了贝塞尔（与高斯合作）的贡献。高斯脑海中的对数积分在复杂分析（Cauchy's Theorem），数值方法（Gaussian Quadrature）以及其与Prime数字的分布等几个领域中发挥了基本作用。我们从Legendre和Tchebycheff到Riemann的作品开始详细研究最后一个方面。
We show the relevance of the logarithmic integral function in the development of mathematics in the first half of the 19th century. Its importance involved first level mathematicians such as Euler, Gauss, Bessel, Riemann. Our perspective is the result of a detailed study of the original sources. We manage to establish the timeline of how the advances took place. In particular, our study vindicates the contributions of Bessel (in collaboration with Gauss). The logarithmic integral in Gauss's mind played a fundamental role in several fields such as complex analysis (Cauchy's theorem), numerical methods (Gaussian quadrature) as well as its best known relation with the distribution of prime numbers. We study this last aspect in detail starting from the works by Legendre and Tchebycheff up to Riemann.
