Simultaneous Integer Values of Pairs of Quadratic Forms
Number Theory
2013-09-27 v1
Abstract
We prove that a pair of integral quadratic forms in 5 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.
Keywords
Cite
@article{arxiv.1309.6767,
title = {Simultaneous Integer Values of Pairs of Quadratic Forms},
author = {D. R. Heath-Brown and L. B. Pierce},
journal= {arXiv preprint arXiv:1309.6767},
year = {2013}
}
Comments
63 pages