Positive values of inhomogeneous quadratic forms of signature −2
✍ Scribed by Satish K. Aggarwal; D.P. Gupta
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 1011 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
The minimum \(\Gamma_{r, n-r}\) of positive values of non-homogeneous indefinite quadratic forms of type \((r, n-r)\) is defined as the infimum of all constants \(\Gamma>0\) such that for any indefinite quadratic form \(Q\) of type ( \(r, n-r\) ) and determinant \(D \neq 0\) and any real numbers \(c
We consider actions of SLð2; ZÞ and SLð2; ZÞ þ (semigroup of matrices with nonnegative integral entries) on the projective space P and on P Â P. Results are obtained on orbit-closures under these actions and they are applied to describe a class of binary quadratic forms Q such that the sets QðZ 2 Þ
A conjecture of G. L. Watson asserts that the two-sided infimum of the values of a non-homogeneous real indefinite quadratic form in \(n\) variables, obtained when the variables range over all integral values, is an invariant under the signature modulo 8. There is an analogous conjecture by Bambah,