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Algebraic dynamics of certain Gamma function values

Borwein, Jonathan M. and Karamanos, Kostas (2005) Algebraic dynamics of certain Gamma function values. In: Generalized Convexity and Generalized Monotonicity, Nonconvex Optimization and its Applications. Springer, Eberhard, Andrew; Hadjisavvas, Nicolas; Luc, Dinh The (Eds.) , pp. 3-21. ISBN 0-387-23638-4

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      Abstract

      We present significant numerical evidence, based on the entropy analysis by lumping of the binary expansion of certain values of the Gamma function, that some of these values correspond to incompressible algorithmic information. In particular, the value $\Gamma(1/5)$ corresponds to a peak of non-compressibility as anticipated on a priori grounds from number-theoretic considerations. Other fundamental constants are similarly considered. This work may be viewed as an invitation for other researchers to apply information theoretic and decision theory techniques in number theory and analysis.

      Item Type: Book Section
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: dynamical systems, Feigenbaum, entropy, normality, Gamma function
      Subjects: 94-xx Information and communication, circuits > 94Axx Communication, information
      37-xx Dynamical systems and ergodic theory > 37Bxx Topological dynamics
      11-xx Number theory > 11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 12 Feb 2004
      Last Modified: 01 Mar 2015 16:03
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/256

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