On representing the multiple of a number by a quadratic form

• Autorzy: Todd Cochrane
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 63
• Numer: 3
• Strony: 211-222

Daty

wydano

1993

otrzymano

1990-11-23

poprawiono

1992-06-16

Twórcy

autor

Todd Cochrane

• Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602, U.S.A.

Bibliografia

• [1] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York 1966.
• [2] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, New York 1978.
• [3] T. Cochrane, Small solutions of congruences over algebraic number fields, Illinois J. Math. 31 (1987), 618-625.
• [4] T. Cochrane, Small zeros of quadratic congruences modulo pq, Mathematika 37 (1990), 261-272.
• [5] T. Cochrane, Small zeros of quadratic forms modulo p, III, J. Number Theory 37 (1) (1991), 92-99.
• [6] D. Grant, Small solutions to a given quadratic form with a variable modulus, to be published.
• [7] D. R. Heath-Brown, Small solutions of quadratic congruences, Glasgow Math. J. 27 (1985), 87-93.
• [8] D. R. Heath-Brown, Small solutions of quadratic congruences, II, Mathematika 38 (1991), 264-284.
• [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.
• [10] J. W. Sander, A reciprocity formula for quadratic forms, Monatsh. Math. 104 (1987), 125-132.
• [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.
• [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.
• [13] G. L. Watson, Integral Quadratic Forms, Cambridge University Press, London 1960.
• [14] G. L. Watson, The minimum of an indefinite quadratic form with integral coefficients, J. London Math. Soc. 32 (1957), 503-507.
• [15] G. L. Watson, Bounded representations of integers by quadratic forms, Mathematika 4 (1957), 17-24.