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Simultaneous integer values of pairs of quadratic forms

Publication ,  Journal Article
Heath-Brown, DR; Pierce, LB
Published in: Journal fur die Reine und Angewandte Mathematik
June 1, 2017

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.

Duke Scholars

Published In

Journal fur die Reine und Angewandte Mathematik

DOI

EISSN

1435-5345

ISSN

0075-4102

Publication Date

June 1, 2017

Volume

2017

Issue

727

Start / End Page

85 / 143

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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Heath-Brown, D. R., & Pierce, L. B. (2017). Simultaneous integer values of pairs of quadratic forms. Journal Fur Die Reine Und Angewandte Mathematik, 2017(727), 85–143. https://doi.org/10.1515/crelle-2014-0112
Heath-Brown, D. R., and L. B. Pierce. “Simultaneous integer values of pairs of quadratic forms.” Journal Fur Die Reine Und Angewandte Mathematik 2017, no. 727 (June 1, 2017): 85–143. https://doi.org/10.1515/crelle-2014-0112.
Heath-Brown DR, Pierce LB. Simultaneous integer values of pairs of quadratic forms. Journal fur die Reine und Angewandte Mathematik. 2017 Jun 1;2017(727):85–143.
Heath-Brown, D. R., and L. B. Pierce. “Simultaneous integer values of pairs of quadratic forms.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 2017, no. 727, June 2017, pp. 85–143. Scopus, doi:10.1515/crelle-2014-0112.
Heath-Brown DR, Pierce LB. Simultaneous integer values of pairs of quadratic forms. Journal fur die Reine und Angewandte Mathematik. 2017 Jun 1;2017(727):85–143.
Journal cover image

Published In

Journal fur die Reine und Angewandte Mathematik

DOI

EISSN

1435-5345

ISSN

0075-4102

Publication Date

June 1, 2017

Volume

2017

Issue

727

Start / End Page

85 / 143

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics