Abstract Analytic Number Theory

This book is well-written and the bibliography excellent declared Mathematical Reviews of John Knopfmacher's innovative study. The three-part treatment applies classical analytic number theory to a wide variety of mathematical subjects not usually treated in an arithmetical way. The first part deals with arithmetical semigroups and algebraic enumeration problems; Part Two addresses arithmetical semigroups with analytical properties of classical type; and the final part explores analytical properties of other arithmetical systems.Because of its careful treatment of fundamental concepts and theorems this text is accessible to readers with a moderate mathematical background i.e. three years of university-level mathematics. An extensive bibliography is provided and each chapter includes a selection of references to relevant research papers or books. The book concludes with an appendix that offers several unsolved questions with interesting proposals for further development.