Analytic Number Theory

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/.

Contents:Calculus of Arithmetic FunctionsSummatory FunctionsThe Distribution of Prime NumbersAn Elementary Proof of the PNTDirichlet Series and Mellin TransformsInversion FormulasThe Riemann Zeta FunctionPrimes in Arithmetic ProgressionsApplications of CharactersOscillation TheoremsSievesApplication of SievesAppendix: Results from Analysis and Algebra
Readership: Graduate students, academics and researchers interested in analytic number theory.