Density of integer solutions to diagonal quadratic forms

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Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)

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 contributionDensity of integer solutions to diagonal quadratic forms
Original languageEnglish
Pages (from-to)13 - 38
Number of pages26
JournalMonatshefte für Mathematik
Volume152
DOIs
Publication statusPublished - Sept 2007

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