Bateman P.T., Diamond H.G. Analytic Number Theory: An Introductory Course

Singapore: World Scientific Publishing, 2004. — 375p. — ISBN: 981-238-938-5; 981-256-080-7Calculus of Arithmetic Functions
Summatory Functions
The Distribution of Prime Numbers
An Elementary Proof of the P.N.T.
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