Titlebook: Selberg Zeta Functions and Transfer Operators; An Experimental Appr Markus Szymon Fraczek Book 2017 Springer International Publishing AG 20

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Markus Szymon FraczekThe only book on the market which describes the evaluation of Selberg zeta functions for character deformations via the transfer operator method.Gives a detailed description of numerical methods and a

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Introduction,s made significant progress, in both analytical investigations and numerical investigations. We consider transfer operators for the geodesic flow on surfaces of constant negative curvature, therefore systems where a particle is moving freely on such a surface with constant velocity.

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Computation of the Spectra and Eigenvectors of Large Complex Matrices,escribe briefly what problems arise when computing the eigenvalues of the transfer operator and how we can overcome these problems. To get the best results, both with respect to accuracy and computation time, we had to combine several techniques to produce an optimal algorithm.

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The Hurwitz Zeta Function and the Lerch Zeta Function,putation of the spectrum of the transfer operator. The implementations of these zeta functions are in a sense the heart of our computations, so we need to be very careful. Unfortunately we have found approximations of these zeta functions in the literature which are quite limited; this is the case e

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The Hyperbolic Laplace-Beltrami Operator,re comprehensive description of the relevant material. Hejhal’s books about the Selberg trace formula [.] and [.] are a source of exhaustive informations regarding most topics discussed in this chapter, these books are most useful for researches already familiar with most of the concepts. Iwaniec’s

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Transfer Operators for the Geodesic Flow on Hyperbolic Surfaces,nction. The transfer operators we are interested in are a so-called . of order zero, these operators have a well defined trace and can be approximated by operators of finite rank. Transfer operators can be also regarded as ., for which an explicit trace formula can be found.

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Concluding Remarks,known even to the experts. Clearly, one of our basic results is the symmetries of the transfer operator in Sect.?. whose existence we found by investigating a new form of the transfer operator that we derived in Lemma?.. This form allows us to write down explicitly the action of the transfer operato