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Low-dimensional lattices. V: Integral coordinates for integral lattices. (English) Zbl 0699.10035

[For part IV see ibid. 419, No.1857, 259-286 (1988; Zbl 0655.10023).]
Given a natural number s, what is the smallest \(n=\phi(s)\) for which there exists a positive definite integral quadratic form f(x) in n variables such that no \(g(x)=x^ 2_ 1+...+x^ 2_ k\), \(k\geq n\), represents \(sf(x)\)? It is shown that \(\phi(1)=6\) (a result of Ko and Mordell), \(\phi(2)=12\), \(\phi(3)=14\), \(21\leq \phi(4)\leq 25,...\), and also some general bounds on \(\phi(s)\) are given.
Reviewer: H.G.Quebbemann

MSC:

11E16 General binary quadratic forms
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
11E12 Quadratic forms over global rings and fields

Citations:

Zbl 0655.10023
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