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Density of integer solutions to diagonal quadratic forms

T. D. Browning

math.NTarXiv:math/0603569

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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