Consider the group
with
On considère le groupe
où
@article{JTNB_2005__17_1_301_0, author = {Christian Roettger}, title = {Counting invertible matrices and uniform distribution}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {301--322}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {1}, year = {2005}, doi = {10.5802/jtnb.492}, mrnumber = {2152226}, zbl = {1101.11011}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.492/} }
TY - JOUR AU - Christian Roettger TI - Counting invertible matrices and uniform distribution JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 301 EP - 322 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.492/ DO - 10.5802/jtnb.492 LA - en ID - JTNB_2005__17_1_301_0 ER -
%0 Journal Article %A Christian Roettger %T Counting invertible matrices and uniform distribution %J Journal de théorie des nombres de Bordeaux %D 2005 %P 301-322 %V 17 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.492/ %R 10.5802/jtnb.492 %G en %F JTNB_2005__17_1_301_0
Christian Roettger. Counting invertible matrices and uniform distribution. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 301-322. doi : 10.5802/jtnb.492. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.492/
[1] A. F. Beardon, The geometry of discrete groups. Springer, 1983. | MR | Zbl
[2] R. W. Bruggeman, R. J. Miatello, Estimates of Kloosterman sums for groups of real rank one. Duke Math. J. 80 (1995), 105–137. | MR | Zbl
[3] C. J. Bushnell, Norm distribution in Galois orbits. J. reine angew. Math. 310 (1979), 81–99. | MR | Zbl
[4] W. Duke, Z. Rudnick, P. Sarnak, Density of integer points on affine homogeneous varieties. Duke Math. J. 71 (1993), 143–179. | MR | Zbl
[5] G. Everest, Diophantine approximation and the distribution of normal integral generators. J. London Math. Soc. 28 (1983), 227–237. | MR | Zbl
[6] G. Everest, Counting generators of normal integral bases. Amer. J. Math. 120 (1998), 1007–1018. | MR | Zbl
[7] G. Everest, K. Györy, Counting solutions of decomposable form equations. Acta Arith. 79 (1997), 173–191. | MR | Zbl
[8] E. Hlawka, Funktionen von beschränkter Variation in der Theorie der Gleichverteilung (German). Ann. Mat. Pura Appl., IV. Ser. (1961), 325–333. | MR | Zbl
[9] E. Hlawka, Theorie der Gleichverteilung. Bibliographisches Institut, Mannheim 1979. | MR | Zbl
[10] L. Kuipers and H. Niederreiter, Uniform distribution of sequences. Wiley, New York 1974. | MR | Zbl
[11] P. Lax and R. Phillips, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. J. Funct. Anal. 46 (1982), 280–350. | MR | Zbl
[12] R. W. K. Odoni, P. G. Spain, Equidistribution of values of rational functions
[13] I. Pacharoni, Kloosterman sums on number fields of class number one. Comm. Algebra 26 (1998), 2653–2667. | MR | Zbl
[14] S. J. Patterson, The asymptotic distribution of Kloosterman sums. Acta Arith. 79 (1997), 205–219. | MR | Zbl
[15] C. Roettger, Counting normal integral bases in complex
[16] C. Roettger, Counting problems in algebraic number theory. PhD thesis, University of East Anglia, Norwich, 2000.
[17] P. Samuel, Algebraic Number Theory. Hermann, Paris 1970. | Zbl
[18] C. L. Siegel, Lectures on the geometry of numbers. Springer, 1989. | MR | Zbl
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