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 

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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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