과제정보
The author is grateful to Pablo Azar, Noam D. Elkies, Andrea J. Hawksley, Sonia Jaffe, Paul M. Kominers, and especially Ravi Jagadeesan for helpful comments and suggestions, and particularly thanks an anonymous referee for pointing out a problem with the original form of Proposition 3.2.
참고문헌
- 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.
- 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.
- 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.
- 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. https://doi.org/10.1098/rspa.1988.0072
- 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. https://doi.org/10.5802/jtnb.848
- 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.
- 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.
- K. Kim and J. Lee and B.-K. Oh, Minimal universality criterion sets on the representations of quadratic forms, (2020), preprint, arXiv:2009.04050.
- S. D. Kominers, Uniqueness of the 2-universality criterion, Note Mat., 28(2)(2008), 203-206.
- J. Lee, Minimal S-universality criterion sets, Seoul National University, Thesis (Ph.D.), 2020.
- B.-K. Oh, Universal Z-lattices of minimal rank, Proc. Amer. Math. Soc., 128(3)(2000), 683-689.
- O. T. O'Meara, Introduction to quadratic forms, Springer-Verlag, New York, 2000.