Browse > Article
http://dx.doi.org/10.5666/KMJ.2021.61.3.455

Oh's 8-Universality Criterion is Unique  

Kominers, Scott Duke (Harvard Business School, Department of Economics, and Center of Mathematical Sciences and Applications, Harvard University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.3, 2021 , pp. 455-459 More about this Journal
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.
Keywords
n-universal lattice; 8-universal lattice; universality criteria; quadratic form; additively indecomposable;
Citations & Related Records
연도 인용수 순위
  • Reference
1 K. Kim and J. Lee and B.-K. Oh, Minimal universality criterion sets on the representations of quadratic forms, (2020), preprint, arXiv:2009.04050.
2 S. D. Kominers, Uniqueness of the 2-universality criterion, Note Mat., 28(2)(2008), 203-206.
3 B.-K. Oh, Universal Z-lattices of minimal rank, Proc. Amer. Math. Soc., 128(3)(2000), 683-689.
4 O. T. O'Meara, Introduction to quadratic forms, Springer-Verlag, New York, 2000.
5 J. Lee, Minimal S-universality criterion sets, Seoul National University, Thesis (Ph.D.), 2020.
6 B. M. Kim and M.-H. Kim and B.-K. Oh, A finiteness theorem for representability of quadratic forms by forms, J. Reine Angew. Math., 581(2005), 23-30.
7 M. Bhargava, On the Conway-Schneeberger fifteen theorem, Quadratic forms and their applications (Dublin, 1999), 27-37, Contemp. Math. 272, Amer. Math. Soc., Providence, RI, 2000.
8 J. H. Conway, Universal quadratic forms and the fifteen theorem, Quadratic forms and their applications (Dublin, 1999), 2326, Contemp. Math. 272, Amer. Math. Soc., Providence, RI, 2000.
9 J. H. Conway and N. J. A. Sloane, Low-dimensional lattices I. Quadratic forms of small determinant, Proc. Roy. Soc. London Ser. A, 418(1854)(1988), 17-41.   DOI
10 B. M. Kim and M.-H. Kim and B.-K. Oh, 2-universal positive definite integral quinary quadratic forms, Integral quadratic forms and lattices (Seoul, 1998), 5162, Contemp. Math. 249, Amer. Math. Soc., Providence, RI, 1999.
11 W. K. Chan and B.-K. Oh, On the exceptional sets of integral quadratic forms, Int. Math. Res. Notices, https://doi.org/10.1093/imrn/rnaa382.   DOI
12 N. D. Elkies, D. M. Kane and S. D. Kominers, Minimal S-universality criteria may vary in size, J. Th'eor. Nombres Bordeaux, 25(3)(2013), 557-563.   DOI