新Dirichlet级数Σn=0∞aneλns的收敛横坐标

The Abscissa of Convergence on the Dirichlet SeriesΣn=0∞aneλns

本文给出新Dirichlet级数Σn=0^∞ane^λns的收敛横坐标σc、一致收敛横坐标σu和绝对收敛横坐标σa的定义.通过指数λn和系数an的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σn=0^∞ane^λns和Σn=0^∞ane^-λns的收敛条件是一致的.

We define the abscissa of convergence σc, the uniform abscissa of convergence σu and the absolute abscissa of convergence σa on Dirichlet seriesΣn=0^∞ane^λns,use the relationship between the index λn and the coefficients an to estimate the three convergence abscissas, and obtain that the convergence conditions of two Dirichlet series（Σn=0^∞ane^λns andΣn=0^∞ane^-λns are the same.