The Exponential World

TL;DR

This book provides a conceptual overview of transcendental number theory, covering foundational ideas and recent frontiers, with an emphasis on understanding rather than technical detail.

Contribution

It offers a comprehensive, accessible introduction to transcendental number theory, focusing on conceptual understanding and recent developments, while omitting detailed effective and special function theories.

Findings

Covers foundational concepts of transcendental number theory

Highlights recent frontiers in the field

Provides an accessible overview for learners

Abstract

In this book there will be found an introduction to transcendental number theory, starting at the beginning and ending at the frontiers. The emphasis is on the conceptual aspects of the subject, thus the effective theory has been more or less completely ignored, as has been the theory of $E$-functions and $G$-functions. Still, a fair amount of ground is covered and while I take certain results without proof, this is done primarily so as not to get bogged down in technicalities, otherwise the exposition is detailed and little is left to the reader.