Convergence tests on constant Dirichlet series

By means of the theory of mathematical analysis, this paper derives the convergence tests for the following two kinds of constant Dirichlet series and an improper integral: ∑n=1∞p(n)ϕ[ψ(n)+δ(n)],∑n=1∞(−1)n−1ϕ[ψ(n)+δ(n)]and∫1∞p(t)ϕ[ψ(t)+δ(t)]dt. As applications, we give two assertions to demonstrate the effectiveness of these convergence tests.