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Existence of Genera in Quadratic Fields

In: The Theory of Algebraic Number Fields

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  • David Hilbert

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.

Suggested Citation

  • David Hilbert, 1998. "Existence of Genera in Quadratic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 18, pages 133-147, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03545-0_18
    DOI: 10.1007/978-3-662-03545-0_18
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