Dirichlet Series, The Growth And The Regular Growth,

This thesis deals with the growth of Dirichlet series in the three aspects:1. The growth and regular growth of Dirichlet series.2. On the (R) order zero of Dirichlet series.3. On the rearrangement of the coefficients of Dirichlet series.The obtained results in this paper weaken the pioneer's conditions, and improve the known results.In Chapter two, a pioneer's growth condition is weakened about analytic Dirichlet series, and an equivalent condition about regular growth in the whole plane is obtained. The growth and regular growth about proximate (R) order of Dirichlet series with infinite ρ order is studied. The obtained results improve some knownresults.In Chapter three, some growth conditions with proximate zero(R) order are weakened for entire and analytic Dirichlet series, and some better results are obtained.In Chapter four, some coefficients rearrangement conditions are obtained respectively for the proximate order, the type of proximate order, the p-order, the type of p-proximate order, the (p,q) (R) order, the type of (p,q) (R) order and the regular growth of Dirichlet series.