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Density of integer solutions to diagonal quadratic forms

T. D. Browning
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Abstract

Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q=0, which lie in a box with sides of length 2B, as B tends to infinity. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.

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T. D. Browning. 2007-04-10. Density of integer solutions to diagonal quadratic forms. https://arxiv.org/abs/math/0603569

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