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 goes to infinity. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.
|Translated title of the contribution||Density of integer solutions to diagonal quadratic forms|
|Pages (from-to)||13 - 38|
|Number of pages||26|
|Journal||Monatshefte für Mathematik|
|Publication status||Published - Sep 2007|