Dirichlet Series And Their Generating Functions

This article mainly discusses Riemann zeta functions which are a special class of generating functions for Dirichlet series. By introducing generating functions and their Euler products of Dirichlet series, we state the generating function of the Euler products for arithmetical functions. Through the generalization of Riemann zeta functions over number fields and function fields, we summarize some analytical properties of the Riemann zeta function and some basic properties related to Weil’s conjecture. Finally, we give some applications of the Riemann zeta function over function fields in algebra-geometric codes.