Integral matrices of fixed rank

Author:
Yonatan R. Katznelson

Journal:
Proc. Amer. Math. Soc. **120** (1994), 667-675

MSC:
Primary 11H06; Secondary 11P21

DOI:
https://doi.org/10.1090/S0002-9939-1994-1169034-3

MathSciNet review:
1169034

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Abstract: Asymptotic formulæare derived for the number of matrices of fixed rank with rational integral coefficients that are contained in a Euclidean ball of radius in . It is assumed that are fixed, and the asymptotics are valid as tends to infinity. The methods used are elementary.

**[Cas]**J. W. S. Cassels,*An introduction to the geometry of numbers*, Springer-Verlag, New York, 1971. MR**0306130 (46:5257)****[DRS]**W. Duke, Z. Rudnick, and P. Sarnak,*Density of integer points on affine homogeneous varieties*, Duke Math J. (to appear). MR**1230289 (94k:11072)****[Kat]**Y. Katznelson,*Singular matrices and a uniform bound for congruence groups of*, Duke Math. J.**69**(1993), 121-136. MR**1201694 (94g:11083)****[Sch]**W. Schmidt,*Asymptotic formulae for point lattices of bounded determinant and subspaces of bounded height*, Duke Math J.**35**(1968), 327-339. MR**0224562 (37:161)****[Sgl]**C. L. Siegel,*Lectures on the geometry of numbers*, Springer-Verlag, New York, 1988. MR**1020761 (91d:11070)****[Ter]**A. Terras,*Harmonic analysis on symmetric spaces and applications*. II, Springer-Verlag, New York, 1988. MR**955271 (89k:22017)**

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1169034-3

Article copyright:
© Copyright 1994
American Mathematical Society