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Markov processes on the adeles and Chebyshev function


  • Yasuda, Kumi


Markov processes on the ring of adeles are constructed, as the limits of Markov chains on some countable sets consisting of subsets of the direct product of real and p-adic fields. As particular cases, we have adelic valued semistable processes. Then it is shown that the values of the Chebyshev function, whose asymptotics is closely related to the zero-free region of the Riemann zeta function, are represented by the expectation of the first exit time for these processes from the set of finite integral adeles.

Suggested Citation

  • Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:238-244
    DOI: 10.1016/j.spl.2012.09.008

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    References listed on IDEAS

    1. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    2. Albeverio, Sergio & Karwowski, Witold, 1994. "A random walk on p-adics--the generator and its spectrum," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 1-22, September.
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    Cited by:

    1. Cruz-López, Manuel & Estala-Arias, Samuel & Murillo-Salas, Antonio, 2016. "A random walk on the profinite completion of Z," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 130-138.

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    Markov processes; Adeles; Riemann zeta function;


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