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Classification of real quadratic forms: A counter-example to finiteness. (Classification des formes quadratiques réelles: Un contre-exemple à la finitude.) (French) Zbl 0811.11047

A relative version of Voronoi’s algorithm for the classification of perfect quadratic forms, developed in [A.-M. Bergé, J. Martinet and F. Sigrist, Astérisque 209, 137-158 (1992; Zbl 0812.11037)] does not necessarily lead to a finite list of inequivalent relatively perfect forms. We give a family of examples in dimension 2, showing that the classification can be finite, infinite with finitely many equivalence classes, or infinite with infinitely many classes.

MSC:

11H55 Quadratic forms (reduction theory, extreme forms, etc.)

Citations:

Zbl 0812.11037
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