From Hermite to Minkowski

  • Winfried Scharlau
  • Hans Opolka
Part of the Undergraduate Texts in Mathematics book series (UTM)


In Chapter 6 we saw that the theory of binary quadratic forms is essentially equivalent to the theory of quadratic number fields. After Gauss, number theory developed in two basically different directions, the theory of algebraic number fields, i.e., finite extensions of ℚ as generalizations of quadratic number fields, and the theory of (integral) quadratic forms in several variables and their automorphisms, as a generalization of binary quadratic forms. In this chapter, we will sketch the development of certain aspects of the latter. To do this, we have to introduce a few basic concepts; for the sake of simplicity, we will use modern terminology.


Basis Vector Lattice Point Number Field Fundamental Domain Algebraic Number Theory 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Winfried Scharlau
    • 1
  • Hans Opolka
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterWest Germany

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