Perfect quadratic forms and problems of arithmetic minima of quadratic forms. (Russian) Zbl 0675.10022

Gametskij, A. F.

Mat. Issled. 103, 22-42 (1988).

The paper introduces the notion of perfect indefinite quadratic form (PIQF). To each PIQF there correspond some convex polyhedra which are connected with the representations of the minimum of the given perfect form. Binary PIQF with two common representations of the minimum are discussed in the paper.

Reviewer: G.Gogishvili

MSC:

11H55	Quadratic forms (reduction theory, extreme forms, etc.)
11H06	Lattices and convex bodies (number-theoretic aspects)

Keywords:

perfect indefinite quadratic form; convex polyhedra; representations; minimum; perfect form