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I am planning to learn some classical results on analytic number theory. I have read Apostol's Introduction to Analytic Number Theory, but nothing about algebraic number theory. Can anyone recommend some more advanced books with further results on analytic number theory?

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Are you aware that Apostol: Introduction to Analytic Number Theory. continues with Volume 2, Modular Functions and Dirichlet Series in Number Theory.

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Yes, Davenport's book (Multiplicative Number Theory) is great, as is Serre's (Course in Arithmetic) Once you read those, check out Iwaniec/Kowalski.

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