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Oh's 8-Universality Criterion is Unique

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We partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh's 8-universality criterion [11] as a corollary.

Abstract

We partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh's 8-universality criterion [11] as a corollary.

참고문헌 (12)

  1. M. Bhargava, "Quadratic forms and their applications", pp.27~37 (2000), Amer. Math. Soc
  2. W. K. Chan, "On the exceptional sets of integral quadratic forms", Int. Math. Res. Notices[DOI]
  3. J. H. Conway, "Quadratic forms and their applications" (2000), Amer. Math. Soc
  4. J. H. Conway, "Low-dimensional lattices I. Quadratic forms of small determinant", Proc. Roy. Soc. London Ser. A, 418(1854), pp.17~41 (1988)
  5. N. D. Elkies, "Minimal S-universality criteria may vary in size", J. Th´eor. Nombres Bordeaux, 25(3), pp.557~563 (2013)
  6. B. M. Kim, "Integral quadratic forms and lattices" (1999), Amer. Math. Soc
  7. B. M. Kim, "A finiteness theorem for representability of quadratic forms by forms", J. Reine Angew. Math, 581, pp.23~30 (2005)
  8. K. Kim, "Minimal universality criterion sets on the representations of quadratic forms", preprint, arXiv:2009.04050, ~ (2020)
  9. S. D. Kominers, "Uniqueness of the 2-universality criterion", Note Mat, 28(2), pp.203~206 (2008)
  10. J. Lee, "Minimal S-universality criterion sets", Ph.D., pp.2020
  11. B. -K. Oh, "Universal Z-lattices of minimal rank", Proc. Amer. Math. Soc, 128(3), pp.683~689 (2000)
  12. O. T. O’Meara, "Introduction to quadratic forms" (2000), Springer-Verlag

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