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.



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> 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.
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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.



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> Should I cover more analytic number theory and less of other topics in pure mathematics?
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I am badly in need of advice/ guidance on this and will be really thankful!



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> If you want any more detail about anything just comment.
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Advice: What topics to study now in analytic number Theory( And if there are video lectures( Open Online course) / Course notes available on website)
(I'm posting this as an answer since I prefer to mantain my anonymity, thus I cannot comment.)


I'm also from a third-world country. At the age of 24, when I was finishing my master's thesis, I was diagnosed with bipolar disorder, and I was drinking way too much. It took me years to recover from alcoholism and to handle my depression. There were three things that kept me alive: the few people that kept around me and cared about me, teaching (part-time), and studying number theory (and that is why I'm posting this comment). Basically, it was the only thing that I was passionate about at that time. It helped me a lot to focus on positive things and to avoid depressing thoughts.


Now I'm in my 30s, and finishing my phd on number theory, and I couldn't be happier. So, dear anon, please stay positive about the future, stay away from illegal drugs and alcohol, be responsible with your treatment (I hope you find a good doctor), and keep studying what you love, in this case number theory.


More important, respect your recovery processes. It is way more important to be healthy mentally (and physically, as far as possible), than anything else.


