Cesaro asymptotics for the orders of SL_k(Z_n)$ and GL_k(Z_n) as n -> infinity
| dc.creator | Gorinov, Alexey G. | |
| dc.creator | Shadchin, Sergey V. | |
| dc.date | 2003-07-02 | |
| dc.date.accessioned | 2026-07-07T04:59:22Z | |
| dc.date.available | 2026-07-07T04:59:22Z | |
| dc.description | Given an integer k>0, our main result states that the sequence of orders of the groups SL_k(\Z_n) (respectively, of the groups GL_k(Z_n)) is Cesaro equivalent as n -> infinity to the sequence C_1(k) n^{k^2-1} (respectively, C_2(k)n^{k^2}), where the coefficients C_1(k) and C_2(k) depend only on k; we give explicit formulas for C_1(k) and C_2(k). This result generalizes the theorem (which was first published by I. Schoenberg) that says that the Euler function is Cesaro equivalent to n * 6/pi^2. We present some experimental facts related to the main result. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307034 | |
| dc.identifier | http://arxiv.org/abs/math/0307034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67956 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | Cesaro asymptotics for the orders of SL_k(Z_n)$ and GL_k(Z_n) as n -> infinity | |
| dc.type | text |