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Algebraic Dynamics of Certain Gamma Function Values

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Generalized Convexity, Generalized Monotonicity and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 77))

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 Γ(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 ah invitation for other researchers to apply information theoretic and decision theory techniques in number theory and analysis.

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Author information

Authors and Affiliations

  1. Computer Science Faculty, Dalhousie University, Canada

    J. M. Borwein (Research Chair)

  2. Centre for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Belgium

    K. Karamanos

Authors
  1. J. M. Borwein
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  2. K. Karamanos
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Editor information

Editors and Affiliations

  1. RMIT University, Australia

    Andrew Eberhard

  2. University of the Aegean, Greece

    Nicolas Hadjisavvas

  3. University of Avignon, France

    Dinh The Luc

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Borwein, J.M., Karamanos, K. (2005). Algebraic Dynamics of Certain Gamma Function Values. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds) Generalized Convexity, Generalized Monotonicity and Applications. Nonconvex Optimization and Its Applications, vol 77. Springer, Boston, MA. https://doi.org/10.1007/0-387-23639-2_1

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