Timeline for Asymptotic number of invertible matrices with integer entries
Current License: CC BY-SA 3.0
3 events
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| Jun 19, 2012 at 5:49 | comment | added | Gerry Myerson | OP asks about "invertible matrices in $M_r$." I take that to mean matrices in $M_r$ with inverses in $M_r$. You don't. Which one of us is right is unclear, especially in light of the $1/(2r+1)$ OP gets in the case $n=1$, which is not consistent with either interpretation. Only OP knows what was intended, and until OP clarifies, we don't really know what OP wants. | |
| Jun 19, 2012 at 3:34 | comment | added | Igor Rivin | The case of $SL(2, Z)$ is analyzed in a paper of Morris Newman's from around 1990 -- notice that this is NOT the question the OP is asking, since he cares about matrices invertible over the reals, not over $\mathbb{Z}$ The Newman result is generalized greatly in the very well-known paper of W. Duke, Z. Rudnick, and P. Sarnak, and the paper of Katznelson I cite is a sort of a follow-up (Katznelson was a student of Sarnak's at the time, and this was his thesis). | |
| Jun 19, 2012 at 2:12 | history | answered | Gerry Myerson | CC BY-SA 3.0 |