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
APA
Chicago
ICMJE
MLA
NLM
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.
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