In this paper we use potential theoretic arguments to establish new results concerning the overconvergence of Dirichlet series. Let \({\sum }_{j=0}^{\infty } a_{j}e^{-\lambda _{j}s}\) converge on the half-plane {Re(s) > 0} to a holomorphic function f. Our first result gives sufficient conditions for a subsequence of partial sums of the series to converge at every regular point of f. The second result shows, in particular, that if a subsequence of the partial sums of the series is uniformly bounded on a nonpolar compact set K ⊂{Re(s) < 0} and ξ ∈{Re(s) = 0} is a regular point of f, then this subsequence converges on a neighbourhood of ξ.

在本文中，我们使用潜在的理论论据来建立有关Dirichlet级数过度收敛的新结果。让\（{\ sum} _ {j = 0} ^ {\ infty} a_ {j} e ^ {-\ lambda _ {j} s} \}收敛于半平面{Re（s）> 0}到全纯函数f。我们的第一个结果为系列的部分和的子序列在f的每个规则点收敛提供了充分的条件。第二结果显示，特别是，如果该系列的部分和的一个子序列被均匀地在非极性紧集界定ķ ⊂{的Re（小号）<0}和ξ＆Element; {的Re（小号）= 0}是一个f的正则点，则该子序列收敛于ξ的邻域。