Geodesic
On a quantitative version of the Oppenheim conjecture
Eskin, Alex1 ; Margulis, Gregory2 ; Mozes, Shahar3
1 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
2 Department of Mathematics, Yale University, New Haven, CT, USA
3 Institute of Mathematics, Hebrew University, Jerusalem 91904, ISRAEL
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 3, pp. 124-130.

Voir la notice de l'article provenant de la source American Mathematical Society

The Oppenheim conjecture, proved by Margulis in 1986, states that the set of values at integral points of an indefinite quadratic form in three or more variables is dense, provided the form is not proportional to a rational form. In this paper we study the distribution of values of such a form. We show that if the signature of the form is not $(2,1)$ or $(2,2)$, then the values are uniformly distributed on the real line, provided the form is not proportional to a rational form. In the cases where the signature is $(2,1)$ or $(2,2)$ we show that no such universal formula exists, and give asymptotic upper bounds which are in general best possible.
DOI : 10.1090/S1079-6762-95-03006-X

Eskin, Alex 1 ; Margulis, Gregory 2 ; Mozes, Shahar 3

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
2 Department of Mathematics, Yale University, New Haven, CT, USA
3 Institute of Mathematics, Hebrew University, Jerusalem 91904, ISRAEL 
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Eskin, Alex; Margulis, Gregory; Mozes, Shahar. On a quantitative version of the Oppenheim conjecture. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 3, pp. 124-130. doi : 10.1090/S1079-6762-95-03006-X. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-03006-X/

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