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