Conway, J. H.; Sloane, N. J. A. Low-dimensional lattices. V: Integral coordinates for integral lattices. (English) Zbl 0699.10035 Proc. R. Soc. Lond., Ser. A 426, No. 1871, 211-232 (1989). [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 Cited in 2 ReviewsCited in 16 Documents MSC: 11E16 General binary quadratic forms 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11E12 Quadratic forms over global rings and fields Keywords:integral lattice; unimodular lattice; eutactic star; quadratic form Citations:Zbl 0655.10023 PDFBibTeX XMLCite \textit{J. H. Conway} and \textit{N. J. A. Sloane}, Proc. R. Soc. Lond., Ser. A 426, No. 1871, 211--232 (1989; Zbl 0699.10035) Full Text: DOI Online Encyclopedia of Integer Sequences: The orders, with repetition, of the non-cyclic finite simple groups that are subquotients of the automorphism groups of sublattices of the Leech lattice.