Simultaneous integer values of pairs of quadratic forms
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.
Heath-Brown, DR; Pierce, LB
Volume / Issue
Start / End Page
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)