JOURNAL BROWSE
Search
Advanced SearchSearch Tips
UNIVERSAL QUADRATIC FORMS OVER POLYNOMIAL RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
UNIVERSAL QUADRATIC FORMS OVER POLYNOMIAL RINGS
Kim, Myung-Hwan; Wang, Yuanhua; Xu, Fei;
  PDF(new window)
 Abstract
The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the Four Conjecture proposed by Gerstein.
 Keywords
universal forms over polynomial rings;the Four conjecture;
 Language
English
 Cited by
1.
UNIVERSAL QUATERNARY LATTICES OVER F q[x],;

East Asian mathematical journal , 2012. vol.28. 5, pp.605-615 crossref(new window)
1.
UNIVERSAL QUATERNARY LATTICES OVER F q[x], East Asian mathematical journal , 2012, 28, 5, 605  crossref(new windwow)
 References
1.
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 crossref(new window)

2.
D. Z. Djokovic, Hermitian matrices over polynomial rings, J. Algebra 43 (1976), no. 2, 359-374 crossref(new window)

3.
W. Duke, Some old problems and new results about quadratic forms, Notices Amer. Math. Soc. 44 (1997), no. 2, 190-196

4.
L. Gerstein, On representation by quadratic $\mathbb{F}_{q}$[x]-lattices, Algebraic and arithmetic theory of quadratic forms, 129-134, Contemp. Math., 344, Amer. Math. Soc., Providence, RI, 2004 crossref(new window)

5.
M.-H. Kim, Recent developments on universal forms, Algebraic and arithmetic theory of quadratic forms, 215-228, Contemp. Math., 344, Amer. Math. Soc., Providence, RI, 2004 crossref(new window)

6.
B. M. Kim, M.-H. Kim, and B.-K. Oh, 2-universal positive definite integral quinary quadratic forms, Integral quadratic forms and lattices (Seoul, 1998), 51-62, Contemp. Math., 249, Amer. Math. Soc., Providence, RI, 1999 crossref(new window)

7.
B. M. Kim, 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

8.
M. Kneser, Darstellungsmasse indefiniter quadratischer Formen, Math. Z. 77 (1961), 188-194 crossref(new window)

9.
W. Leahey, Sums of squares of polynomials with coefficients in a finite field, Amer. Math. Monthly 74 (1967), 816-819 crossref(new window)

10.
O. T. O'Meara, The integral representations of quadratic forms over local fields, Amer. J. Math. 80 (1958), 843-878 crossref(new window)

11.
O. T. O'Meara, Introduction to Quadratic Forms, Springer-Verlag, Berlin, 2000

12.
W. Schneeberger, Arithmetic and geometry of integral lattices, Ph.D. Thesis, Princeton University, 1995