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Article: Automorphisms of polynomial algebras and Dirichlet series

TitleAutomorphisms of polynomial algebras and Dirichlet series
Authors
Drensky, VYu, JT
KeywordsAutomorphisms
Coordinates
Dirichlet Series
Finite Fields
Free Associative Algebras
Generating Functions
Nielsen-Schreier Varieties
Polynomial Algebras
Issue Date2009
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2009, v. 321 n. 1, p. 292-302 How to Cite?
DOI: http://dx.doi.org/10.1016/j.jalgebra.2008.08.026
AbstractLet Fq [x, y] be the polynomial algebra in two variables over the finite field Fq with q elements. We give an exact formula and the asymptotics for the number pn of automorphisms (f, g) of Fq [x, y] such that max {deg (f), deg (g)} = n. We describe also the Dirichlet series generating functionp (s) = under(∑, n ≥ 1) frac(pn, ns) . The same results hold for the automorphisms of the free associative algebra Fq 〈 x, y 〉. We have also obtained analogues for free algebras with two generators in Nielsen-Schreier varieties of algebras. © 2008 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156233
ISSN
0021-8693
2023 Impact Factor: 0.8
2023 SCImago Journal Rankings: 1.023
ISI Accession Number ID
WOS:000261590100016
Funding AgencyGrant Number
Vesselin DrenskyMI-150312005
Bulgarian National Science
RGC-CERG
Funding Information:

The research of Vesselin Drensky was partially supported by Grant MI-150312005 of the Bulgarian National Science Fund.

References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:57Z-
dc.date.available2012-08-08T08:40:57Z-
dc.date.issued2009en_US
dc.identifier.citationJournal Of Algebra, 2009, v. 321 n. 1, p. 292-302en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156233-
dc.description.abstractLet Fq [x, y] be the polynomial algebra in two variables over the finite field Fq with q elements. We give an exact formula and the asymptotics for the number pn of automorphisms (f, g) of Fq [x, y] such that max {deg (f), deg (g)} = n. We describe also the Dirichlet series generating functionp (s) = under(∑, n ≥ 1) frac(pn, ns) . The same results hold for the automorphisms of the free associative algebra Fq 〈 x, y 〉. We have also obtained analogues for free algebras with two generators in Nielsen-Schreier varieties of algebras. © 2008 Elsevier Inc. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectAutomorphismsen_US
dc.subjectCoordinatesen_US
dc.subjectDirichlet Seriesen_US
dc.subjectFinite Fieldsen_US
dc.subjectFree Associative Algebrasen_US
dc.subjectGenerating Functionsen_US
dc.subjectNielsen-Schreier Varietiesen_US
dc.subjectPolynomial Algebrasen_US
dc.titleAutomorphisms of polynomial algebras and Dirichlet seriesen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepreprinten_US
dc.identifier.doi10.1016/j.jalgebra.2008.08.026en_US
dc.identifier.scopuseid_2-s2.0-55949135469en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-55949135469&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume321en_US
dc.identifier.issue1en_US
dc.identifier.spage292en_US
dc.identifier.epage302en_US
dc.identifier.eissn1090-266X-
dc.identifier.isiWOS:000261590100016-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US
dc.identifier.issnl0021-8693-

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