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Communications in Mathematical Physics

, Volume 160, Issue 3, pp 493–505 | Cite as

The variance of the error function in the shifted circle problem is a wild function of the shift

  • Pavel M. Bleher
  • Freeman J. Dyson
Article

Abstract

We prove that the variance of the error function in the shifted circle problem, as a function of the shift, is a continuous function which has a sharp local maximum with infinite derivatives at every rational point on a plane.

Keywords

Neural Network Statistical Physic Continuous Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Pavel M. Bleher
    • 1
  • Freeman J. Dyson
    • 1
  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA

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