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Dirichlet 字符\(\chi \)的p进L函数\(L_p(s,\chi )\)。我们证明，\(L_p(s,\chi )\)对于与p和\(\chi \)的导体互质的每个正则化参数c具有狄利克雷级数展开式。通过变换p进L函数的已知公式并控制极限行为来证明展开式。有限数量的欧拉因子可以以自然的方式从p进狄利克雷级数中分解出来。我们还提供了使用p进测量的展开式的替代证明，并给出了正则化伯努利分布值的显式公式。对于\(c=2\) ，结果特别简单，我们获得了与复杂情况类似的狄利克雷级数展开式。