Summary: In this paper, we define the abscissa of convergence \({\sigma_c}\), the uniform abscissa of convergence \({\sigma_u}\) and the absolute abscissa of convergence \({\sigma_a}\) on Dirichlet series \(\sum {_{n = 0}^\infty {a_n}{e^{{\lambda_n}s}}} \). Then we use the relationship between the index \({\lambda_n}\) and the coefficients \({a_n}\) to estimate the three convergence abscissas, and obtain that the convergence conditions of two Dirichlet series \(\sum {_{n = 0}^\infty {a_n}{e^{{\lambda_n}s}}} \) and \(\sum {_{n = 0}^\infty {a_n}{e^{ - {\lambda_n}s}}} \) are the same.