Markov processes on the adeles and Chebyshev function

Kumi Yasuda

Statistics & Probability Letters, 2013, vol. 83, issue 1, 238-244

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.

Keywords: Markov processes; Adeles; Riemann zeta function (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2012.09.008

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