Simultaneous integer values of pairs of quadratic forms
Journal Article (Journal Article)
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.
Full Text
Duke Authors
Cited Authors
- Heath-Brown, DR; Pierce, LB
Published Date
- June 1, 2017
Published In
Volume / Issue
- 2017 / 727
Start / End Page
- 85 - 143
Electronic International Standard Serial Number (EISSN)
- 1435-5345
International Standard Serial Number (ISSN)
- 0075-4102
Digital Object Identifier (DOI)
- 10.1515/crelle-2014-0112
Citation Source
- Scopus