Oppenheim conjecture for pairs consisting of a linear form and a quadratic form

A Gorodnik

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

7 Citations (Scopus)

Abstract

Let Q be a nondegenerate quadratic form and L a nonzero linear form of dimension d > 3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x); L(x)) : x is an element of Z(d)} is dense in R-2 provided that Q and L satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.
Translated title of the contributionOppenheim conjecture for pairs consisting of a linear form and a quadratic form
Original languageEnglish
Pages (from-to)4447 - 4463
Number of pages17
JournalTransactions of the American Mathematical Society
Volume356 (11)
Publication statusPublished - Nov 2004

Bibliographical note

Publisher: American Mathematical Soc

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