3 papers
math.NT2017
Hyperbolicity over function fields of quadrics
James O'Shea
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolici…
math.NT2015
Multiples of Pfister forms
James O'Shea
The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the values of their first Witt indices is obtained. A number of corollaries of this…
math.NT2012
Isotropy of multiples of Pfister forms and weak isotropy of forms over field extensions
James O'Shea
The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its cor…