Cesàro asymptotics for the orders of SLk(Zn) and GLk(Zn) as n→∞

✍ Scribed by Alexey G Gorinov; Sergey V Shadchin

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 98 KB
• Volume: 337
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(03)00328-5

✦ Synopsis

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

, 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 ϕ(n) is Cesàro equivalent to n 6 π 2 . We present some experimental facts related to the main result.