dc.creatorCesaratto, Eda
dc.creatorVallée, Brigitte
dc.date.accessioned2022-08-23T18:30:12Z
dc.date.accessioned2022-10-15T12:54:07Z
dc.date.available2022-08-23T18:30:12Z
dc.date.available2022-10-15T12:54:07Z
dc.date.created2022-08-23T18:30:12Z
dc.date.issued2021-10
dc.identifierCesaratto, Eda; Vallée, Brigitte; Gaussian Behavior of Quadratic Irrationals; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 197; 2; 10-2021; 159-205
dc.identifier0065-1036
dc.identifierhttp://hdl.handle.net/11336/166385
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/4388381
dc.description.abstractWe study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with the underlying dynamical system associated with the Gauss map, and its weighted periodic trajectories. We work with analytic combinatorics methods, and mainly with bivariate Dirichlet generating functions; we use various tools, from number theory (the Landau Theorem), from probability (the Quasi-Powers Theorem), or from dynamical systems: our main object of study is the (weighted) transfer operator, that we relate with the generating functions of interest. The present paper exhibits a strong parallelism with the methods which have been previously introduced by Baladi and Vallée in the study of rational trajectories. However, the present study is more involved and uses a deeper functional analysis framework.
dc.languageeng
dc.publisherPolish Academy of Sciences. Institute of Mathematics
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.48550/arXiv.1708.00051
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.00051
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectQUADRATIC IRRATIONALS
dc.subjectCONTINUED FRACTIONS
dc.subjectTRANSFER OPERATORS
dc.subjectANALYTIC COMBINATORICS
dc.subjectDIRICHLET SERIES
dc.subjectCENTRAL LIMIT THEOREM
dc.subjectLANDAU THEOREM
dc.titleGaussian Behavior of Quadratic Irrationals
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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