Original Articles

ANALYTIC AND PROBABILISTIC THEORY OF ADDITIVE ARITHMETICAL SEMIGROUPS

Published in: Quaestiones Mathematicae
Volume 24 , issue 3 , 2001 , pages: 323–333

DOI: 10.1080/16073606.2001.9639221

Author(s): Wen-Bin Zhang Department of Mathematics, USA

Keywords: Primary: 11N60 , Secondary: 11T55 , 30B30 , 60F05 , Primary: 11N60 , Secondary: 11T55 , 30B30 , 60F05

Abstract

This is a short survey of the forthcoming book Number Theory Arising From Finite Fields—analytic and probabilistic theory. We give details of a number of the main theorems in the book. These are abstract prime number theorems, mean-value theorems of multiplicative functions, infinitely divisible distributions and central limit theorems. We also highlight new research directions.

« CONTRIBUTIONS TO ABSTRACT ANALYTIC NUMBER THEORY

DISTRIBUTION OF MULTIPLICATIVE FUNCTIONS DEFINED ON SEMIGROUPS »