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The Dedekind zeta function and the class number formula

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Number Fields

Part of the book series: Universitext ((UTX))

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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 = . 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

  • eBook Packages: Springer Book Archive

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