Markov processes on the adeles and chebyshev function

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8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)238-244
Number of pages7
JournalStatistics and Probability Letters
Volume83
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Keywords

  • Adeles
  • Markov processes
  • Riemann zeta function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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