HOMOGENEOUS FORM INEQUALITIES (I) : VOLUME ESTIMATES AND THE GENERALISED METRIC OPPENHEIM CONJECTURE
This is the first part of a work devoted to the study of the set of integer solutions to a system of inequalities determined by homogeneous forms. According to the heuristics that the number of such solutions should match the volume of the set of real solutions, sharp estimates for the volume of the semialgebraic domain under consideration are established. These estimates are expressed as a functi
