Values of Non-homogeneous Indefinite Quadratic Forms Original Research Article

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, Dumir, and Hans- Gill concerning the one-sided infimum. It is shown how both conjectures follow from the result of Margulis on forms not commensurable with a rational form combined with results of G. L. Watson on rational forms.