Kyoto Journal of Mathematics

Bohr–Jessen process and functional limit theorem

Satoshi Takanobu

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The Bohr–Jessen limit theorem states that for each σ>12, there exists an asymptotic probability distribution of logζ(σ+-1). Here ζ() is the Riemann zeta function, and logζ() is a primitive function of ζ'/ζ on some simply connected domain of C. In this paper, we generalize this limit theorem to a functional limit theorem and show a similar limit theorem for a continuous process {logζ(σ+-1)}σ>1/2, which we call the Bohr–Jessen functional limit theorem.

Article information

Kyoto J. Math., Volume 54, Number 2 (2014), 401-426.

First available in Project Euclid: 2 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$


Takanobu, Satoshi. Bohr–Jessen process and functional limit theorem. Kyoto J. Math. 54 (2014), no. 2, 401--426. doi:10.1215/21562261-2642440.

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