The Growth Of Dirichlet Series Of Zero Order

This thesis deals with the growth of Dirichlet series of zero order in the two aspects:1.The growth of Dirichlet series of zero order in the half plane 2.The growth of Dirichlet series of zero order in the whole plane In one part,The relation between the maximum modulus and maximum term of Dirichlet series of zero order in the right half-complex plane is obtained. And we have an equivalent condition about the growth of Dirichlet series of zero order in the half plane.Furthmore,the result is improved to the lower order.In two part,with the induction of function U,the relation between the maximum modulus and the coefficients,exponent of Dirichlet series of zero order in the whole plane is studied. The obtained results improve some known results.