High Quality Content by WIKIPEDIA articles! In mathematics, the Dedekind zeta-function is a Dirichlet series defined for any algebraic number field K, and denoted K(s) where s is a complex variable. It is the infinite sum where I ranges through the non-zero ideals of the ring of integers OK of K. Here NK/Q(I) = [OK : I] denotes the norm of I. It is equal to the cardinality of OK / I, in other words, the number of residue classes modulo I. This sum converges absolutely for all complex numbers s with real part Re(s) > 1. In the case K = Q this definition reduces to the Riemann zeta function. The properties of K(s) as a meromorphic function turn out to be of considerable significance in algebraic number theory

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.