罗伯特·詹逖生在幂级数部分列零点理论上的工作研究

利用历史分析和文献考证的方法,探讨罗伯特·詹逖生(Jentzsch R,1890-1918)在幂级数部分列零点理论方面的工作,揭示其思想方法和重要影响.詹逖生在1914年的博士论文中提出了关于幂级数部分列零点的两个重要定理,一个是幂级数收敛圆上的每个点为其部分列零点的聚点;另一个是部分列零点数目的定量描述.在1917年的论文中,他通过具体例子说明了级数超收敛的思想.詹逖生在此方面的工作奠定了幂级数部分列零点理论研究的基础,对斯泽古(Szego G,1895-1985)、Dvoretzky A、奥斯特洛斯基(Ostrowski A,1893-1986)等人有重要影响.

Robert Jentzsch＇s Work on the Zeros Theory of Partial Sums of Power Series

Jentzsch R＇s work on the zeros theory of partial sums of power series is discussed,and thoughts and influence are shown by historical analysis and literature review.Jentzsch R proposed two theories of the zeros theory of partial sums of power series in his doctoral dissertation of 1914.The one is that every point on the circle of convergence is a cluster point of zeros of the partial sums;the other is about the quantitative information on the location of those zeros.He studied the overconvergence of the series by the examples in 1917.His work plays an important role on zeros of the partial sums and influence on Szego G、Dvoretzky A and Ostrowski A.