I'm a physics graduate recently learned Riemann hypothesis in a mathematical physics course. ( I knew what the hypothesis is but didn't know mathematical statement)
I got interested, and I wanna study more about Riemann zeta function and Riemann hypothesis. I don't dare to solve it, just wanna taste it.
I've learned basic complex analysis, and calculus, linear algebra(though seems not related on this), but not number theory.
Recently I borrowed a book named 'The music of primes' but I found it was too verbose even though the writer was a mathematician. (I know, the book was for laypeople)
I want mathematical approach, but I know that I have no ability to read professional papers or like that, so I would like to start with the appropriate prerequisite branch of mathematics.
Can you suggest what mathematical branch is related to the Riemann hypothesis? And if you can suggest proper textbooks which I can study by myself it would be appreciated.
Best Answer
Most books on analytic number theory mention the Riemann zeta function in one way or another. In fact, there is a nice Dover book (so it's fairly cheap) called Riemann's Zeta Function by Edwards: https://www.amazon.com/Riemanns-Zeta-Function-Harold-Edwards/dp/0486417409 -- that's a place to start anyway. It goes through the basics, and beyond, and only presupposes some knowledge of one variable complex analysis.