by Paul T Bateman (University of Illinois at Urbana-Champaign) & 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.

Comments and corrigenda for the book are found at http://www.math.uiuc.edu/~diamond/.

• 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