On representing the multiple of a number by a quadratic form

Todd Cochrane

Acta Arithmetica (1993)

  • Volume: 63, Issue: 3, page 211-222
  • ISSN: 0065-1036

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Todd Cochrane. "On representing the multiple of a number by a quadratic form." Acta Arithmetica 63.3 (1993): 211-222. <http://eudml.org/doc/206517>.

@article{ToddCochrane1993,
author = {Todd Cochrane},
journal = {Acta Arithmetica},
keywords = {representations; small multiples; quadratic form; local-to-global principles},
language = {eng},
number = {3},
pages = {211-222},
title = {On representing the multiple of a number by a quadratic form},
url = {http://eudml.org/doc/206517},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Todd Cochrane
TI - On representing the multiple of a number by a quadratic form
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 3
SP - 211
EP - 222
LA - eng
KW - representations; small multiples; quadratic form; local-to-global principles
UR - http://eudml.org/doc/206517
ER -

References

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  1. [1] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York 1966. 
  2. [2] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, New York 1978. 
  3. [3] T. Cochrane, Small solutions of congruences over algebraic number fields, Illinois J. Math. 31 (1987), 618-625. Zbl0608.12001
  4. [4] T. Cochrane, Small zeros of quadratic congruences modulo pq, Mathematika 37 (1990), 261-272. Zbl0713.11030
  5. [5] T. Cochrane, Small zeros of quadratic forms modulo p, III, J. Number Theory 37 (1) (1991), 92-99. Zbl0713.11031
  6. [6] D. Grant, Small solutions to a given quadratic form with a variable modulus, to be published. Zbl0770.11021
  7. [7] D. R. Heath-Brown, Small solutions of quadratic congruences, Glasgow Math. J. 27 (1985), 87-93. Zbl0581.10008
  8. [8] D. R. Heath-Brown, Small solutions of quadratic congruences, II, Mathematika 38 (1991), 264-284. Zbl0725.11018
  9. [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. [10] J. W. Sander, A reciprocity formula for quadratic forms, Monatsh. Math. 104 (1987), 125-132. Zbl0627.10012
  11. [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. Zbl0446.10026
  12. [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. Zbl54.0178.01
  13. [13] G. L. Watson, Integral Quadratic Forms, Cambridge University Press, London 1960. Zbl0090.03103
  14. [14] G. L. Watson, The minimum of an indefinite quadratic form with integral coefficients, J. London Math. Soc. 32 (1957), 503-507. Zbl0079.06806
  15. [15] G. L. Watson, Bounded representations of integers by quadratic forms, Mathematika 4 (1957), 17-24. Zbl0077.26402

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