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