Simultaneous integer values of pairs of quadratic forms

Abstract

Abstract We prove that a pair of integral quadratic forms in five or more variables will simultaneously represent “almost all” pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.

Locations

• arXiv (Cornell University) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View