| Abstract: | We treat systems of real diagonal forms  of degree  , in  variables. We give a lower bound  , which depends only on  and  , such that if  holds, then, under certain conditions on the forms, and for any positive real number  , there is a nonzero integral simultaneous solution  of the system of Diophantine inequalities  for  . In particular, our result is one of the first to treat systems of inequalities of even degree. The result is an extension of earlier work by the author on quadratic forms. Also, a restriction in that work is removed, which enables us to now treat combined systems of Diophantine equations and inequalities. |
