Positive values of indefinite quadratic forms

Cook, R. J. ; Raghavan, S. (1986) Positive values of indefinite quadratic forms Mathematika, 33 (1). pp. 164-169. ISSN 0025-5793

Full text not available from this repository.

Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S0025579300013978


Let f(x)= ∑ n i=1n j=1 fijxixj (fij= fji) (1) be a real quadratic form in n variables with integral coefficients (i.e., 2fijε Z,fij ε Z.) and determinant D ≠ O. A well-known theorem of Cassels [1] states that if the equation f = 0 is properly soluble in integers x1 … , xn then there is a solution satisfying 0<||x||=max|xi≪ F(n-1)/2, (2). ∏ni=1||x|| ≪ Fn(n-1)/2+(n-2)/2, (3).

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:10C25; Number Theory; Forms; Minima Of Forms
ID Code:86760
Deposited On:12 Mar 2012 15:46
Last Modified:12 Mar 2012 15:46

Repository Staff Only: item control page