On Values of Linear and Quadratic Forms at Integral Points

S. G. Dani

Type: Book-Chapter

Publication Date: 2000-01-01

Citations: 12

DOI: https://doi.org/10.1007/978-3-0348-7023-8_6

Abstract

The aim of this article is to give an exposition of certain applications of the study of the homogeneous space SL(n, ℝ)/SL(n, ℤ) and the flows on it induced by subgroups of SL(n, ℝ),to problems on values of linear and quadratic forms at integral points. Also, some complements to Margulis's theorem on Oppenheim's conjecture are proved.

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+	Flows on homogeneous spaces and Diophantine properties of matrices	1998	Dmitry Kleinbock
+	Geometry of Numbers	1987	Peter M. Gruber
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+	Introduction to Diophantine Approximations	1995	Serge Lang
+	Unipotent Flows and Counting Lattice Points on Homogeneous Varieties	1996	Alex Eskin Shahar Mozes Nimish A. Shah
+	An Introduction to Diophantine Approximation.	1958	John C. Brixey J. W. S. Cassels
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