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Proofs Based on the Theory of Quadratic Forms

In: The Quadratic Reciprocity Law

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  • Oswald Baumgart

Abstract

Recall that the complex of all equivalent forms of the same discriminant is called a form class form class. If the integers a, b, c in the form1 (a, b, c) are coprime, then the form is called primitive. form primitive If the [greatest common] divisor σ of a, 2b, c is 1, then (a, b, c) is called a form form first kind of the first kind, and if σ = 2 it is called a form of the second form second kind kind. An ambiguous form ambiguous form2 is a form in which the double middle coefficient 2b is divisible by the first. The form (1, 0, −D) is called the principal form principal form of discriminant D; its class is called the principal class principal class. If the outer coefficients of a form are positive, then the form itself is called positive. form positive

Suggested Citation

  • Oswald Baumgart, 2015. "Proofs Based on the Theory of Quadratic Forms," Springer Books, in: The Quadratic Reciprocity Law, edition 127, chapter 0, pages 63-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16283-6_6
    DOI: 10.1007/978-3-319-16283-6_6
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