Cesàro asymptotics for the orders of SLk(Zn) and GLk(Zn) as n→∞ |
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Authors: | Alexey G Gorinov Sergey V Shadchin |
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Institution: | 1. Université Paris 7, U.F.R. de mathématiques, 2, place Jussieu, 75251, France;2. IHES, Bures-sur-Yvette, route de Chartres, 91140, France |
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Abstract: | Given an integer k>0, our main result states that the sequence of orders of the groups (respectively, of the groups ) is Cesàro equivalent as n→∞ to the sequence C1(k)nk2?1 (respectively, C2(k)nk2), where the coefficients C1(k) and C2(k) depend only on k; we give explicit formulas for C1(k) and C2(k). This result generalizes the theorem (which was first published by I. Schoenberg) that says that the Euler function ?(n) is Cesàro equivalent to . We present some experimental facts related to the main result. To cite this article: A.G. Gorinov, S.V. Shadchin, C. R. Acad. Sci. Paris, Ser. I 337 (2003). |
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