Values of isotropic quadratic forms at S -integral points

Armand Borel; Gopal Prasad

Compositio Mathematica (1992)

  • Volume: 83, Issue: 3, page 347-372
  • ISSN: 0010-437X

How to cite


Borel, Armand, and Prasad, Gopal. "Values of isotropic quadratic forms at $S$-integral points." Compositio Mathematica 83.3 (1992): 347-372. <>.

author = {Borel, Armand, Prasad, Gopal},
journal = {Compositio Mathematica},
keywords = {minima of forms; density of values; orbit closures; generalization of Margulis' theorem; indefinite quadratic form; small values at integral points},
language = {eng},
number = {3},
pages = {347-372},
publisher = {Kluwer Academic Publishers},
title = {Values of isotropic quadratic forms at $S$-integral points},
url = {},
volume = {83},
year = {1992},

AU - Borel, Armand
AU - Prasad, Gopal
TI - Values of isotropic quadratic forms at $S$-integral points
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 83
IS - 3
SP - 347
EP - 372
LA - eng
KW - minima of forms; density of values; orbit closures; generalization of Margulis' theorem; indefinite quadratic form; small values at integral points
UR -
ER -


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  3. [BP] A. Borel et G. Prasad: Valeurs de formes quadratiques aux points entiers, C. R. Acad. Sci. Paris307 (1988), 217-220. Zbl0654.10022MR956809
  4. [D] S.G. Dani, A simple proof of Borel's density theorem, Math. Zeitschr.174 (1980), 81-94. Zbl0432.22008MR591617
  5. [DM] S.G. Dani and G.A. Margulis: Values of quadratic forms at primitive integral points, Inv. Math.98 (1989), 405-425. Zbl0682.22008MR1016271
  6. [M] G.A. Margulis: Discrete groups and ergodic theory, in Number Theory, Trace Formulas and Discrete Groups, Symposium in honor of A. Selberg, Oslo1987, Academic Press (1989), 377-398. Zbl0675.10010MR993328
  7. [P] V.P. Platonov: The problem of strong approximation and the Kneser-Tits conjecture, Math. USSR Izv.3 (1969), 1139-1147;Addendum, ibid.4(1970), 784-786. Zbl0236.20034
  8. [RR] S. Raghavan and K.G. Ramanathan: On a diophantine inequality concerning quadratic forms, Göttingen Nachr. Mat. Phys. Klasse (1968), 251-262. Zbl0214.06602MR263743
  9. [Rt] M. Ratner: Raghunathan's topological conjecture and distribution of unipotent flowsDuke Math. J.63 (1991), 235-280. Zbl0733.22007MR1106945
  10. [W] A. Weil, Adeles and algebraic groups, Progress in Mathematics23, Birkhäuser, Boston, 1982. Zbl0493.14028MR670072

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