On representing the multiple of a number by a quadratic form
Todd Cochrane
Acta Arithmetica, Tome 64 (1993), p. 211-222 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206517
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     author = {Todd Cochrane},
     title = {On representing the multiple of a number by a quadratic form},
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     volume = {64},
     year = {1993},
     pages = {211-222},
     zbl = {0771.11020},
     language = {en},
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Todd Cochrane. On representing the multiple of a number by a quadratic form. Acta Arithmetica, Tome 64 (1993) pp. 211-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav63i3p211bwm/

[000] [1] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York 1966.

[001] [2] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, New York 1978.

[002] [3] T. Cochrane, Small solutions of congruences over algebraic number fields, Illinois J. Math. 31 (1987), 618-625. | Zbl 0608.12001

[003] [4] T. Cochrane, Small zeros of quadratic congruences modulo pq, Mathematika 37 (1990), 261-272. | Zbl 0713.11030

[004] [5] T. Cochrane, Small zeros of quadratic forms modulo p, III, J. Number Theory 37 (1) (1991), 92-99. | Zbl 0713.11031

[005] [6] D. Grant, Small solutions to a given quadratic form with a variable modulus, to be published. | Zbl 0770.11021

[006] [7] D. R. Heath-Brown, Small solutions of quadratic congruences, Glasgow Math. J. 27 (1985), 87-93. | Zbl 0581.10008

[007] [8] D. R. Heath-Brown, Small solutions of quadratic congruences, II, Mathematika 38 (1991), 264-284. | Zbl 0725.11018

[008] [9] Yu. V. Linnik and A. V. Malyshev, An elementary proof of the Kloosterman-Tartakovskiĭ theorem on the representations of numbers by positive quadratic forms, in: Proc. Fourth All-Union Math. Congr., Leningrad 1961, Vol. II, Nauka, Leningrad 1964, 116-117.

[009] [10] J. W. Sander, A reciprocity formula for quadratic forms, Monatsh. Math. 104 (1987), 125-132. | Zbl 0627.10012

[010] [11] A. Schinzel, H. P. Schlickewei and W. M. Schmidt, Small solutions of quadratic congruences and small fractional parts of quadratic forms, Acta Arith. 37 (1980), 241-248. | Zbl 0446.10026

[011] [12] W. A. Tartakowsky [V. A. Tartakovskiĭ], La détermination de la totalité des nombres représentables par une forme quadratique à plus de quatre variables, C. R. Acad. Sci. Paris 186 (1928), 1337-1340, 1401-1403, 1684-1687. Errata to second paper: 187 (1928), 155. | Zbl 54.0178.01

[012] [13] G. L. Watson, Integral Quadratic Forms, Cambridge University Press, London 1960. | Zbl 0090.03103

[013] [14] G. L. Watson, The minimum of an indefinite quadratic form with integral coefficients, J. London Math. Soc. 32 (1957), 503-507. | Zbl 0079.06806

[014] [15] G. L. Watson, Bounded representations of integers by quadratic forms, Mathematika 4 (1957), 17-24. | Zbl 0077.26402