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On Geary’s theorem for the field of p-adic numbers

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Abstract

Let ℚ p , where p > 2, be a field of p-adic numbers. We consider two independent identically distributed random variables with values in ℚ p and distribution μ with a continuous density. We prove that the sum and the squared difference of these random variables are independent if and only if μ is an idempotent distribution, i.e., a shift of the Haar distribution of a compact subgroup of the additive group of the field ℚ p .

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References

  1. R. C. Geary, J. R. Stat. Soc. 3, 178–184 (1936).

    Google Scholar 

  2. E. Lukacs, Ann. Math. Stat. 13, 91–93 (1942).

    Article  MathSciNet  Google Scholar 

  3. T. Kawata and H. Sakamoto, J. Math. Soc. Jpn. 1, 111–115 (1949).

    Article  MathSciNet  Google Scholar 

  4. A. A. Zinger, Usp. Mat. Nauk 6 (5), 172–175 (1951).

    MathSciNet  Google Scholar 

  5. A. M. Kagan, Yu. V. Linnik, and S. R. Rao, Characterization Problems in Mathematical Statistics (Nauka, Moscow, 1972; Wiley, New York, 1973).

    MATH  Google Scholar 

  6. G. M. Feldman, Theory Probab. Appl. 37 (4), 621–631 (1993).

    Article  Google Scholar 

  7. D. Neuenschwander and R. Schott, Exposition. Math. 15, 289–314 (1997).

    MathSciNet  Google Scholar 

  8. G. M. Feldman, Probab. Theory Relat. Fields 126, 91–102 (2003).

    Article  Google Scholar 

  9. G. M. Feldman, Probab. Theory Relat. Fields 133, 345–357 (2005).

    Article  Google Scholar 

  10. G. M. Feldman, Studia Math. 177, 67–79 (2006).

    Article  MathSciNet  Google Scholar 

  11. G. M. Feldman, J. Funct. Anal. 258, 3977–3987 (2010).

    Article  MathSciNet  Google Scholar 

  12. M. Myronyuk, Colloquium Math. 132, 195–210 (2013).

    Article  MathSciNet  Google Scholar 

  13. I. P. Mazur, Ukr. Mat. Zh. 65, 947–961 (2013).

    Article  MathSciNet  Google Scholar 

  14. G. M. Feldman, Functional Equations and Characterization Problems on Locally Compact Abelian Groups (Eur. Math. Soc., Zurich, 2008).

    Book  MATH  Google Scholar 

  15. A. Kagan, R. C. Laha, and V. Rohatgi, Math. Methods Stat. 6, 263–265 (1997).

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47, Nauky ave, Kharkiv, 61103, Ukraine

    M. V. Myronyuk & G. M. Feldman

Authors
  1. M. V. Myronyuk
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  2. G. M. Feldman
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Corresponding author

Correspondence to M. V. Myronyuk.

Additional information

Original Russian Text © M.V. Myronyuk, G.M. Feldman, 2016, published in Doklady Akademii Nauk, 2016, Vol. 467, No. 2, pp. 131–134.

The article was translated by the authors.

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Myronyuk, M.V., Feldman, G.M. On Geary’s theorem for the field of p-adic numbers. Dokl. Math. 93, 152–154 (2016). https://doi.org/10.1134/S1064562416020095

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  • DOI: https://doi.org/10.1134/S1064562416020095

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