TITLE: Textbooks for studying Riemann hypothesis
QUESTION [13 upvotes]: 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.

REPLY [2 votes]: In case you are not ware of, here is the
Original statement of RH by Riemann himself .
Based on your math background (basic complex analysis, calculus, linear algebra, but not number theory) and my own experience, I would recommend the following 2 review papers:
(1) "Zeros of entire Fourier transforms" by Dimitrov and Rusev,
East. J. On Approximations, vol. 17, no. 1 (2011): pp 1-108.
(2) P. M. Hallum, "Zeros of Entire Functions Represented by Fourier Transforms", Master Thesis,University of Hawaii at Manoa (2014).
The reasons that I made this recommendation are the following:
I also have a physics background and am interested in studying Riemann Hypothesis. 
For some books I encountered, I found out that they contain too much advanced math (like analytical number theory) than I am familiar with, e.g., (3) "The Theory of the Riemann Zeta-Function" by Titchmarsh, (4) "Riemann Zeta Function" by Edwards and (5) "Introduction to Analytic Number Theory" by Apostol etc.
For other books I encountered, I found out that they contain too little math than I wish to see, e.g.,(6) "Prime Numbers and the Riemann Hypothesis" by Mazur and Stein, (7) "The music of primes" by Marcus du Sautoy.
But reading ref.(1) and ref.(2) does not need the advanced knowledge of analytical number theory. You only need to be familiar with Fourier transform when you start to read ref.(1) and ref.(2). So these two papers just fitted my needs and (I hope) may fit yours as well.   
You can then learn other necessary math subjects as you go from math books or from wikipedia.org (like I did).