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I want to start learning things about the Riemann zeta function, I would like to cover things like its different representations, its universality property and its connections with prime numbers (I know very little about number theory!).

What are some good books on the topic? I'd like to focus exclusively in the $\zeta$ function (and perhaps some topics in analysis required to understand the other content).

YoTengoUnLCD
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  • I haven't read it in some time, but everyone seems to love Edwards' Riemann's Zeta Function. It's now a Dover book, so very cheap. – Hoot Sep 02 '16 at 20:38
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    I might suggest you start with Reimann's actual paper. It is surprisingly readable. http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf – Doug M Sep 02 '16 at 20:48
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    Apostol's book in Analytic Number Theory I think would be ideal, although (extensive) discussion of $\zeta (s) $ doesn't begin until chapter 12. However not all material beforehand is necessary in the book, but you have plenty of problems. Murty's problem book also has plenty of material relating to the zeta function. Finally, Titchmarsh's book is probably the most complete, but fairly advanced (I do not know your current level). – Rellek Sep 02 '16 at 20:58
  • This list of books may be useful, too. – Dietrich Burde Sep 02 '16 at 21:01
  • you also have to study in details a complex analysis course – reuns Sep 03 '16 at 09:16

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