We study p-adic L-functions \(L_p(s,\chi )\) for Dirichlet characters \(\chi \). We show that \(L_p(s,\chi )\) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of \(\chi \). The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for \(c=2\), where we obtain a Dirichlet series expansion that is similar to the complex case.

我们研究p进制大号-functions \（L_P（S，\气）\）对Dirichlet字符\（\卡\） 。我们证明\(L_p(s,\chi )\)对于每个正则化参数c都具有狄利克雷级数展开式，该参数是p 的素数和\(\chi \)的导体。通过转换p- adic L-函数的已知公式并控制极限行为来证明扩展。有限数量的欧拉因子可以自然地从p- adic Dirichlet 级数中分解出来。我们还使用p提供了扩展的替代证明-adic 度量并给出正则化伯努利分布值的明确公式。对于\(c=2\) 而言，结果特别简单，我们获得了类似于复杂情况的狄利克雷级数展开。