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Markov processes on the adeles and Dedekind’s zeta function

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  • Urban, Roman

Abstract

We construct an additive Markov process on the ring of adeles of an algebraic number field and use this process to give a probabilistic interpretation of the Dedekind zeta function. This note extends and clarifies a recent work of Yasuda where the Riemann zeta function was considered.

Suggested Citation

  • Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1583-1589
    DOI: 10.1016/j.spl.2012.04.018
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    References listed on IDEAS

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    1. 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. Estala-Arias, Samuel, 2020. "Pseudodifferential operators and Markov processes on certain totally disconnected groups," Statistics & Probability Letters, Elsevier, vol. 164(C).
    2. 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.
    3. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
    4. Cruz-López, Manuel & Estala-Arias, Samuel, 2018. "A random walk on the profinite completion of a finitely generated group," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 7-16.

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