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 prime number theorems,
mean-value theorems of multiplicative functions, infinitely divisible distributions
and central limit theorems. We also highlight new research directions.
Mathematics Subject Classification (1991): Primary: 11N60; Secondary:
11T55, 30B30, 60F05
Keywords: Additive arithmetical semigroup, number theorem, mean-value
theorem, normal distribution

Quaestiones Mathematicae 24(3) 2001, 323-333