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An introductory book on the Distribution of Prime Numbers and Riemann's Zeta Function

  1. Jul 4, 2012 #1
    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.
     
  2. jcsd
  3. Jul 5, 2012 #2
    Re: An introductory book on the Distribution of Prime Numbers and Riemann's Zeta Func

    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.
     
  4. Jul 6, 2012 #3
    Re: An introductory book on the Distribution of Prime Numbers and Riemann's Zeta Func

    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.
     
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