I have studied analytic number theory from 2 volumes of Apostol , Lectures in Sieve Theory online and I am thinking of reading some research papers in Number Theory and then try to work on some problem (If possible).

The issue is that I don't have a guidence.

So, can you please let me know what are the major different directions of Analytic Number Theory in where research is active now a days along with a very brief explanation of why ?

Thank you very much!

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    $\begingroup$ Even though by now it is almost 20 years old, the Iwaniec-Kowalski book gives a much more modern perspective than Apostol's... although certainly Apostol is a good warm-up, since the I-K book is quite terse in computations. $\endgroup$ Jul 16 at 18:30
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    $\begingroup$ @Arnold, when your questions receive answers, please do not delete them anymore. Think of the fact that the person who answered you spent some time and thinking writing that answer, only for you to delete this whole effort with a click. $\endgroup$
    – Alex M.
    Jul 17 at 7:26
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    $\begingroup$ @AlexM. They never recieved any answers. On Stackexchange Network , any question which recieve answer cannot be deleted. $\endgroup$
    – Arnold
    Jul 17 at 7:47
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    $\begingroup$ I would probably do Montgomery-Vaughan or Koukoulopoulos before tackling I-W (or else I would have chapters of I-K together with either textbook). Apostol tends to be recommended as a first book in analytic number theory by people who are not in analytic number theory, it would seem. $\endgroup$ Jul 20 at 16:50


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