Supplemental number theory text to Montgomery and Vaughan

Solution 1:

Of course, the second book in their sequence: Montgomery and Vaughn Chapters 16-27 draft version (online only)

Here are some other well known titles (in no particular order):

H. Iwaniec and E. Kowalski, Analytic Number Theory

H. Davenport, Multiplicative Number Theory

A. E. Ingham, The Distribution of Prime Numbers

T. M. Apostol, Introduction to Analytic Number Theory

P. T. Bateman and H. G. Diamond, Analytic Number Theory: An introductory course

E. C. Titchmarsh (revised by D. R. Heath-Brown), The Theory of the Riemann Zeta-Function

Hope that helps,

Remark: These books were all suggested readings from one of my courses. The books by Davenport, Bateman, Apostol and Ingham were suggested reading for the basics of analytic number theory, while Titchmarsh and Iwaniec and the online chapters of M&V were more related to the course material.

Solution 2:

I would also add to Eric's answer that Tenenbaum's "Introduction to Analytic and Probabilistic Number" is a great resource if one is limited to the number of books you can carry.