Automorphisms of polynomial algebras and Dirichlet series
| dc.creator | Drensky, Vesselin | |
| dc.creator | Yu, Jie-Tai | |
| dc.date | 2008-06-04 | |
| dc.date | 2008-06-27 | |
| dc.date.accessioned | 2026-07-07T09:46:48Z | |
| dc.date.available | 2026-07-07T09:46:48Z | |
| dc.description | Let GF(q)[x,y] be the polynomial algebra in two variables over the finite field GF(q) with q elements. We give an exact formula and the asymptotics for the number p(n) of automorphisms (f,g) of GF(q)[x,y] such that max{deg(f),deg(g)}=n. We describe also the Dirichlet series generating function p(1)/1^s+p(2)/2^s+p(3)/3^s+.... The same results hold for the automorphisms of the free associative algebra GF(q)<x,y>. We have also obtained analogues for free algebras with two generators in Nielsen - Schreier varieties of algebras. | |
| dc.description | 13 pages, revised version, new results are added | |
| dc.identifier | https://arxiv.org/abs/0806.0681 | |
| dc.identifier | http://arxiv.org/abs/0806.0681 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163655 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11T06; 13B25; 05A15; 30B50; 16S10; 17A50. | |
| dc.title | Automorphisms of polynomial algebras and Dirichlet series | |
| dc.type | text |