Regular and semi-regular positive ternary quadratic forms
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- H. J. S. Smith,Collected Papers, vol. 1, pp. 455–509;Philosophical Transactions, vol. 157, pp. 255–298.
- Jones, B. W. (1931) Trans. Amer. Math. Soc. 33: pp. 92-110 CrossRef
- Two forms are of the sameclass if one may be taken into the other by a linear trans formation withintegral coefficients and of determinant I; i. e. by a unimodular transformation.
- Jones, B. W. (1931) Trans. Amer. Math. Soc. 33: pp. 111-124 CrossRef
- Dickson, L. E. (1927) Annals of Math. 28: pp. 333-341
- Meyer, A. (1891) Journal für Mathematik 108: pp. 125-139
- For references seeDickson,History of the Theory of Numbers, vol. 2.
- Ramanujan, S. (1916) Proc. Cambridge Phil. Soc. 19: pp. 11-21
- B. W. Jones, «The Representation of Integers by Positive Ternary Quadratic Forms», a University of Chicago thesis (1928), unpublished.
- In the thesis the form (1, 5, 200) was erroneously reported to be regular. It fails to represent 44 and hence is irregular. The rest of the table has been checked and found to be correct.
- that isx 2+y 2+16z 2. Similarlyax 2+by 2+cz 2+2ryz+28xz+2txy is denoted by (a, b, c, r, s, t).
- Nazimoff,Applications of the Theory of Elliptic Functions to the Theory of Numbers (Russian) translated by Arnold Chaimovitch. The proof for this form was indicated by Nazimoff and carried out by Chaimovitch.
- Tartakowsky, W. A. (1928) Comptes Rendus de l'Académie des Sciences 186: pp. 1337-1340
- For references seeDickson,History of the Theory of Numbers, vol. 2, pp. 261–3 and p. 268 respectively. For example Glaisher states the following inMessenger of Mathematics, new series vol. 6, (1877), p. 104: The excess of the number of representations of 8n+1 in the formx 2+4y 2+4z 2 withy andz even over the number of representations withy andz odd is zero if 8n+I is not a square and 2(−I)(s−1)/2 s if 8n+I=s 2.
- Pall, Gordon (1937) Amer. Journ. of Math. 59: pp. 895-913 CrossRef
- Eisenstein, (1851) Journal für Mathematik 41: pp. 141-190
- H. J. S. Smith,Collected Papers, vol. 2, p. 635; alsoMémoires présentés par divers Savants à l'Académie des Sciences de l'Institut de France (2), vol. 29 (1887), No. 1, 72 pp. 22–38333.Acta mathematica. 70. Imprimé le 2 décembre 1938.
- B. W. Jones,A New Definition of Genus... see earlier reference.
- Forms so marked are in genera of more than one class.
- Regular and semi-regular positive ternary quadratic forms
Volume 70, Issue 1 , pp 165-191
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