T. D. Browning
Published 2006-03-24, updated 2007-04-10Version 3
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.
Improved upper bounds for the number of points on curves over finite fields
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