Kaplansky, Irving The first nontrivial genus of positive definite ternary forms. (English) Zbl 0826.11015 Math. Comput. 64, No. 209, 341-345 (1995). The author considers the genus of ternary quadratic forms consisting of the classes of the forms \(f= x^2+ y^2+ 7z^2\) and \(g= x^2+ 2y^2+ 2yz+ 4z^2\). Several theorems are proved regarding which of the integers represented by this genus are represented by \(f\), which by \(g\), and which by both \(f\) and \(g\). For the positive integers not exceeding 100,000 which are represented by the genus but are not covered by any of these theorems, the author reports the result of computations determining which of these integers fail to be represented by each of the forms. Reviewer: A.G.Earnest (Carbondale) Cited in 4 ReviewsCited in 8 Documents MSC: 11E25 Sums of squares and representations by other particular quadratic forms 11E20 General ternary and quaternary quadratic forms; forms of more than two variables Keywords:representation; genus; ternary quadratic forms PDFBibTeX XMLCite \textit{I. Kaplansky}, Math. Comput. 64, No. 209, 341--345 (1995; Zbl 0826.11015) Full Text: DOI Online Encyclopedia of Integer Sequences: Numbers not of the form x^2+7*y^2+7*z^2. Numbers not of the form x^2+2*y^2+2*y*z+4*z^2 (with x, y, z all >= 0). Numbers not of the form x^2+y^2+14*z^2. Numbers prime to 7 that are not represented by x^2+y^2+7*z^2. Numbers congruent to 1, 2, or 4 mod 7 that are not represented by x^2+7*y^2+7*z^2. Numbers of the form 8*k+3 not represented by 2*x^2+4*y^2+4*y*z+9*z^2. Numbers not of the form x^2+2*y^2+7*z^2. References: [1] Burton W. Jones, The regularity of a genus of positive ternary quadratic forms, Trans. Amer. Math. Soc. 33 (1931), no. 1, 111 – 124. · JFM 57.0195.03 [2] Burton W. Jones and Gordon Pall, Regular and semi-regular positive ternary quadratic forms, Acta Math. 70 (1939), no. 1, 165 – 191. · Zbl 0020.10701 · doi:10.1007/BF02547347 [3] Gordon Pall, An almost universal form, Bull. Amer. Math. Soc. 46 (1940), 291. · Zbl 0024.24903 [4] -, Representations by quadratic forms, Canad. J. Math. 1 (1949), 344-364. · Zbl 0034.02201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.