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Markov processes on the adeles and Chebyshev function

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  • Yasuda, Kumi
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    Abstract

    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212003458
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 238-244

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:238-244

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    Related research

    Keywords: Markov processes; Adeles; Riemann zeta function;

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    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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