Discovering Prime Numbers & Riemann's Zeta Function

[Karlx]

Hi everybody.
I would like to find a book about the Distribution of Prime Numbers and the Riemann's Zeta Function.

I know about the "classical" books:

1) Titchmarsh's "The Theory of the Riemann Zeta-Function"
2) Ingham's "The Distribution of Prime Numbers"
3) Ivic's "The Riemann Zeta-Function:Theory and Applications"

but I don't know it they are too much complicated or whether there is a much "modern" book that could serve as an introduction.

I've read the book "Prime Obsession" by John Derbyshire, that is an excellent "expository/divulgatory" book about prime numbers and Riemann's Zeta-Function.
I recommend it very much.
But now I would like to go deeper about the matter.
Which book do you recommend me ?

Thanks.

 

[Petek]

You might want to look at the following books. All are more elementary than the first three books that you listed, but are more technical than Derbyshire's book:

Introduction to Analytic Number Theory by Apostol.

Number Theory: An Introduction via the Distribution of Primes by Fine and Rosenberger.

The Prime Number Theorem by Jameson.

All these books require some prior knowledge of basic (undergraduate) real and complex analysis.

 

[Karlx]

Thanks a lot, Petek.
At first glance, Jameson's book seems to me a good choice as an elementary first introduction to the matter.
And Fine and Rosenberger's one seems interesting too.
Apostol appears to me as the more technical of three.


Thanks again.