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arXiv · 1309.6767

Simultaneous Integer Values of Pairs of Quadratic Forms

D. R. Heath-Brown·L. B. Pierce
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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.

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D. R. Heath-Brown, L. B. Pierce. 2013-09-26. Simultaneous Integer Values of Pairs of Quadratic Forms. https://arxiv.org/abs/1309.6767

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