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Bohr-Jessen limit theorem, revisited. (English) Zbl 1364.60011

MSJ Memoirs 31. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-019-8/pbk). xii, 216 p. (2013).
Publisher’s description: This book is a self-contained exposition on the Bohr-Jessen limit theorem. This limit theorem, which is concerned with the behavior of the Riemann zeta function \(\zeta(s)\) on the line \(\mathrm{Re}\, s=\sigma\), where \(1/2<\sigma \leq 1\), was found by Bohr-Jessen in the early 1930s. After Bohr-Jessen, alternative proofs were given by Jessen-Wintner, Borchsenius-Jessen, Laurinčikas, Matsumoto and others. They dealt with this within the framework of probability theory. Their formulation, originated by Jessen-Wintner, is standard nowadays. The present book proposes a new approach for the formulation to refine their works. By this method, the whole story of the proof of the Bohr-Jessen limit theorem will now become clearer, so that the reader must be able to understand the essence of the proof in depth but without difficulty.

MSC:

60B10 Convergence of probability measures
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
60F05 Central limit and other weak theorems
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
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