04041nam 22007575 450 991025738010332120200630020454.03-319-51296-X10.1007/978-3-319-51296-9(CKB)4340000000062305(DE-He213)978-3-319-51296-9(MiAaPQ)EBC6295540(MiAaPQ)EBC5578832(Au-PeEL)EBL5578832(OCoLC)987489830(PPN)201471108(EXLCZ)99434000000006230520170513d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierSelberg Zeta Functions and Transfer Operators An Experimental Approach to Singular Perturbations /by Markus Szymon Fraczek1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XV, 354 p. 71 illus., 43 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;21393-319-51294-3 This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.Lecture Notes in Mathematics,0075-8434 ;2139Number theoryComputer scienceMathematicsApproximation theoryFunctions of complex variablesFunctions, SpecialDynamicsErgodic theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Computational Mathematics and Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M1400XApproximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Functions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Special Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XNumber theory.Computer scienceMathematics.Approximation theory.Functions of complex variables.Functions, Special.Dynamics.Ergodic theory.Number Theory.Computational Mathematics and Numerical Analysis.Approximations and Expansions.Functions of a Complex Variable.Special Functions.Dynamical Systems and Ergodic Theory.515.56Fraczek Markus Szymonauthttp://id.loc.gov/vocabulary/relators/aut742221MiAaPQMiAaPQMiAaPQBOOK9910257380103321Selberg Zeta functions and transfer operators1474428UNINA