Existence of Genera in Quadratic Fields

David Hilbert

Chapter 18 in The Theory of Algebraic Number Fields, 1998, pp 133-147 from Springer

Abstract: Abstract It still remains for us to establish the second part of the fundamental Theorem 100, i.e. to prove that the condition we have just proved necessary for a set of r units ±1 to be the character set of a genus in k $$\left( {\sqrt m } \right)$$ is also sufficient. This proof can be carried out in two completely different ways: the first is purely arithmetic in nature, the second makes essential use of transcendental methods. The first proof is achieved through the following considerations.

Keywords: Prime Number; Prime Ideal; Fundamental Theorem; Principal Ideal; Ideal Class (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-3-662-03545-0_18

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