I am a person living in a 3rd world country and completed my masters in mathematics in July 2020. Then I began to study some additional topics in Pure Mathematics as I was applying for Ph.D. abroad( In Number Theory) as I felt that I should study more topics before applying in December2020- January 2021.

Background in analytic number theory: I have studied Number Theory from Elementary number theory by Burton, Introduction to Analytic Number Theory (Tom Apostol) , Modular Functions and Dirichlet Series in Number Theory ( Tom Apostol).

I am thinking of studying more Analytic number theory in the free time I am having. But instead of studying from textbook I thought of studying from Lecture notes ( If available on course page of course) as when studying from textbook one covers many more topics than required in a course. But if the course is not available in lecture notes form then textbook recommendations are also most welcome.

So, Can you please tell which courses in analytic number theory should I study now and give some suggestions of course pages/ textbooks? I am thinking of covering material equivalent to 2 courses.

In rest of time I am planning to study some topics from other branches of pure mathematics( one of which is Elliptic curves, is it part of analytic number theory?) depending on time available.

Should I cover more analytic number theory and less of other topics in pure mathematics?

I am badly in need of advice/ guidance on this and will be really thankful!

If you want any more detail about anything just comment.

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