Math @ Duke
|
Publications [#320389] of Lillian B. Pierce
Papers Published
- Heath-Brown, DR; Pierce, LB, Simultaneous integer values of pairs of quadratic forms,
Journal fur die Reine und Angewandte Mathematik, vol. 2017 no. 727
(June, 2017),
pp. 85-143, WALTER DE GRUYTER GMBH [doi]
(last updated on 2024/04/17)
Abstract: 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.
|
|
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
| |
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
|
|