ANALYTIC AND PROBABILISTIC THEORY OF ADDITIVE ARITHMETICAL SEMIGROUPS

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.