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 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 |
|---|---|
| Original language | English |
| Pages (from-to) | 13 - 38 |
| Number of pages | 26 |
| Journal | Monatshefte für Mathematik |
| Volume | 152 |
| DOIs | |
| Publication status | Published - Sep 2007 |