ANALYTIC NUMBER THEORY
An Introductory Course
by Paul T Bateman & Harold G Diamond (University of Illinois at Urbana-Champaign)
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable ("elementary") and complex variable ("analytic") methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.
Contents:
- Calculus of Arithmetic Functions
- Summatory Functions
- The
Distribution of Prime Numbers
- An Elementary Proof of the PNT
- Dirichlet Series and Mellin Transforms
- Inversion Formulas
- The Riemann Zeta Function
- Primes in Arithmetic Progressions
- Applications of Characters
- Oscillation Theorems
- Sieves
- Application of Sieves
- Appendix: Results from Analysis and Algebra
Readership: Graduate students, academics and researchers interested in
analytic number theory.
“This book also includes a nice introduction to sieve methods ... Overall, this is a nice well-written book with plenty of material for a one-year graduate course. It would also make nice supplementary reading for a student or researher learning the subject.”
“This is a nice introductory book on analytic number theory for students or readers with some background in real analysis, complex analysis, number theory and abstract algebra … There are various exercises throughout the entire book. Moreover, at the end of each chapter, historical backgrounds and developments of each particular subject or theorem are given together with references.”
“This book is suitable for beginning graduate students, or possibly even advanced undergraduates.”
| 376pp |
Pub. date: Sept 2004 |
