Density of integer solutions to diagonal quadratic forms

Details Density of integer solutions to diagonal quadratic forms Density of integer solutions to diagonal quadratic forms

2006-03-24

arxiv.org/abs/math/0603569v3

Mathematics

Number Theory

23 pages

Scientific paper

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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