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p-Adic dynamics and angle doubling

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Abstract

We consider the squaring map over the p-adic numbers for an odd prime p, and study its symbolic dynamics on the unit circle in ℤ p , the p-adic integers. When the map is restricted to the set of squares, we show an equivalence to angle doubling (mod 1) for rational angles. For primes p ≡ 3 (mod 4), this map may be represented as a unitary permutation matrix of the type used in quantum phase estimation.

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Authors and Affiliations

  1. Mathematics Department, Queens College, CUNY, Flushing, NY, 11367, USA

    M. Maller

  2. Computer Science Department, Queens College, CUNY, Flushing, NY, 11367, USA

    J. Whitehead

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  1. M. Maller
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  2. J. Whitehead
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Correspondence to M. Maller.

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The text was submitted by the authors in English.

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Maller, M., Whitehead, J. p-Adic dynamics and angle doubling. P-Adic Num Ultrametr Anal Appl 5, 14–21 (2013). https://doi.org/10.1134/S2070046613010020

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  • DOI: https://doi.org/10.1134/S2070046613010020

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