I am self studying analytic number theory and I have finished Apostol's Introduction to Analytic Number Theory just now. Now I have started the second volume of Apostol's Dirichlet Series and Modular Forms. But it focuses on additive number theory not multiplicative number theory.
Also, no faculty at my institution is interested in, or works in, analytic number theory. So can someone please suggest a good reference book in multiplicative number theory after Apostol volume 1?
Regarding reference book in multiplicative number theory
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Best Answer
As suggested, Davenport’s Multiplicative Number Theory is a classical text and after Apostol you would be in good shape to grok it.
You may also find helpful J.P. Serre’s A Course in Arithmetic, which is divided into two halves, algebraic and analytic, of which in this case clearly the analytic portion would be of interest.
After you finish Davenport, Analytic Number Theory by Henryk Iwaniec and Emmanuel Kowalski is the classical “next step,” and it is very comprehensive and very good. After that, you will likely be ready for further specialization, and will be best served by beginning to read papers in specific areas of interest.