Bohr-jessen Limit Theorem, Revisited

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 ?(s) on the line Re s = s, where 1/2 < s = 1, was found by Bohr-Jessen in the early 1930s. After Bohr-Jessen, alternative proofs were given by Jessen-Wintner, Borchsenius-Jessen, Laurinckas, 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.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

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 ζ(s) on the line Re s = σ, where 1/2 < σ ≤ 1, was found by Bohr-Jessen in the early 1930s. After Bohr-Jessen, alternative proofs were given by Jessen-Wintner, Borchsenius-Jessen, Laurinčkas, 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.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets