Abstract
We will use the results of chapter 6 to define and establish properties of the Dedekind zeta function of a number ring R. This is a generalization of the familiar Riemann zeta function, which occurs when R = ℤ. Using this function we will determine densities of certain sets of primes and establish a formula for the number of ideal classes in an abelian extension of Q.
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© 1977 Springer-Verlag, New York Inc.
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Marcus, D.A. (1977). The Dedekind zeta function and the class number formula. In: Number Fields. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9356-6_7
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DOI: https://doi.org/10.1007/978-1-4684-9356-6_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90279-1
Online ISBN: 978-1-4684-9356-6
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