Linearly independent zeros of quadratic forms over number-fields |
| |
Authors: | J H H Chalk |
| |
Institution: | (1) Department of Mathematics, University of Toronto, M5S1 A1 Toronto, Canada |
| |
Abstract: | LetK be an algebraic number-field of degree K:Q] =n 1 and letO denote some fixed order ofK. Let, be a quadratic form which represents zero for some. For the special caseK =Q,O =Z, theorems ofCassels and ofDavenport provide estimates for the magnitude (in terms of the coefficients off(x)) of a zero and of a pair of linearly independent zeros off, respectively. Recently,Raghavan extendedCassels' result to arbitraryK. In this article, a new proof ofDavenport's theorem for a pair of linearly independent zeros is given which not only provides explicit constants in the estimates but also extends to generalK. A refinement of this proof leads to effectively computable bounds for rational representations of a numbern0 byf. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|