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

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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.

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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, 08540, Princeton, NJ, USA

    Pavel M. Bleher & Freeman J. Dyson

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  1. Pavel M. Bleher
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  2. Freeman J. Dyson
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Communicated by T. Spencer

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Bleher, P.M., Dyson, F.J. The variance of the error function in the shifted circle problem is a wild function of the shift. Commun.Math. Phys. 160, 493–505 (1994). https://doi.org/10.1007/BF02173426

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  • DOI: https://doi.org/10.1007/BF02173426

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