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Determination of a binary quadratic form by its values at integer points: Acknowledgement

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
G. L. Watson
Affiliation:
Department of Mathematics, University College London, Gower streetLondon WC1E 6BT
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Extract

The result of my paper with the title given above (Mathematika, 26 (1979), 72–75) is not new; it was proved by Delone, see [2] and [3]. I have not been able to refer to either of these papers, but the result is given in [1], A similar problem was considered by Kitaoka in [5]. Professor Kneser of Göttingen tells me that he solved the problem about ten years ago in an unpublished manuscript; also that Schering's result [4] is less general and weaker than mine. I am obliged to Professor Peters of Münster for a copy of [1], giving the references [2] to [4], and also for the reference [5].

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 188
Copyright
Copyright © University College London 1980

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References

1.Timofeev, V. N.. “On positive quadratic forms, representing the same numbers”, Uspekhi Mat. Nauk, 18 (1963), 191–193. 18 (1963), 191–193.Google Scholar
2.Delone, B. N.. “On the unique definition of the fundamental parallelepiped of a crystal structure by the method of Debye”, Letters of the Russian Mineralogical Soc. (1926), (1962).Google Scholar
3.Delone, B. N.. “Geometry of positive quadratic forms, addendum”, Uspechi Mat. Sci, 4 (1938), , YMH, Iv (1938).Google Scholar
4.Schering, M.. “Théorèmes relatifs aux formes quadratiques qui représentent les mêmes nombres”, J. Math, pures el appl, 2 serie 4 (1859).Google Scholar
5.Kitaoka, Y.. “On the relation between the positive-definite quadratic forms with the same representation numbers”, Proc. Jap. Acad., 47 (1971), 439–441.Google Scholar