I am requesting a list of books to learn number theory by myself that would take me from an introduction in the field to being an expert.
I am most interested in understanding unsolved problems in number theory that are in these subfields:
- Prime Numbers (their distribution and other conjectures)
- The Riemann hypothesis
- The Twin prime conjecture
- Prime gap
- Additive number theory
I want a list of books by order of level that I can go through one after the other, as this is a roadmap to learning the field.
P.S: The books should be for self-learning
It would be nice if you can give me the estimated time it would take me to work through each book.