DirichletReihe
Dirichletreihe, named after the German mathematician Peter Gustav Lejeune Dirichlet, is a type of infinite series used primarily in number theory and complex analysis. It is generally expressed in the form:
where a(n) is a complex-valued arithmetic function, and s is a complex variable typically written as s
A prominent example of a Dirichletreihe is the Riemann zeta function ζ(s), which corresponds to the case
Dirichletreihe are fundamental in studying properties of prime numbers, as they encode arithmetic information through their
The convergence, analytic continuation, and functional equations of Dirichletreihe are central topics in modern number theory