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We already have a large list of the Best ever book on Number Theory, but I'm looking for a more targeted response for analytic number theory.

Specifically, I'm taking a trip on which I may or may not have access to internet resources, nor my University's library. I'm starting to work through Montgomery and Vaughan's Multiplicative Number Theory. What would be the one book you recommend bringing as a supplement?

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2 Answers 2

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.

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Excellent list! I've acquired Davenport's text from my library, and I've worked through a few chapters of Ingham during a course last semester. (editing to say 'thanks!') –  John Hammond Apr 4 '11 at 20:12

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.

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Thanks for the mention. I'll look into this one. –  John Hammond Apr 4 '11 at 20:13

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