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Introductory text book on the Riemann Zeta Function

  • 26-09-2011 10:29am
    #1
    Closed Accounts Posts: 130 ✭✭


    Hello to all

    I am looking for a good book on the Riemann Zeta function. Perhaps you can recommend one. I guess it should be at the level of a mathematics student learning the topic for the first time.

    Thank you.


Comments

  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    There are very few books entirely dedicated to just the Riemann zeta function. Apostol's book has a chapter on it. Edwards' book is quite well respected, too. There's also titchmarsh, but that's probably not ideal for a beginner.

    Arguably you're better off learning a load of algebraic number theory for now, and studying the zeta function later.


  • Registered Users, Registered Users 2 Posts: 1,163 ✭✭✭hivizman


    Although it's not a formal textbook, you could read Marcus du Sautoy's The Music of the Primes: Why an Unsolved Problem in Mathematics Matters (Harper Perennial, 2003). If you are after mathematical sophistication, then the book won't be what you want, but if you are looking for something that explains the zeta function in informal terms in the context of number theory, this book is a good general introduction.

    I'd endorse all of Fremen's suggestions. When I studied number theory, the textbook of choice was Hardy & Wright An Introduction to the Theory of Numbers, but I don't know the current edition or whether it addresses the zeta function.


  • Closed Accounts Posts: 130 ✭✭Kohl


    Thanks to you both for your suggestions.


  • Closed Accounts Posts: 4,204 ✭✭✭FoxT


    Meh, a few weeks back I read "Marcus du Sautoy's The Music of the Primes: Why an Unsolved Problem in Mathematics Matters".


    It was....OK. Great on anecdotes about various mathematicians, but really lame when it came to describing the math.

    I finished it b/c I started it, but I wouldn't recommend it to anybody who really wanted to gain an understanding of the Zeta Function.
    -FoxT


  • Moderators, Science, Health & Environment Moderators Posts: 1,852 Mod ✭✭✭✭Michael Collins


    FoxT wrote: »
    Meh, a few weeks back I read "Marcus du Sautoy's The Music of the Primes: Why an Unsolved Problem in Mathematics Matters".


    It was....OK. Great on anecdotes about various mathematicians, but really lame when it came to describing the math.

    I finished it b/c I started it, but I wouldn't recommend it to anybody who really wanted to gain an understanding of the Zeta Function.
    -FoxT

    Hmm this was the next book on my list, it's on my desk in preparation...Now I've just lost all my enthusiasm!


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  • Closed Accounts Posts: 4,204 ✭✭✭FoxT


    Stay enthusiastic - I just hope I may have saved you some time :)


  • Registered Users, Registered Users 2 Posts: 3,745 ✭✭✭Eliot Rosewater


    hivizman wrote: »
    I'd endorse all of Fremen's suggestions. When I studied number theory, the textbook of choice was Hardy & Wright An Introduction to the Theory of Numbers, but I don't know the current edition or whether it addresses the zeta function.

    There's a chapter on arithmetical functions in which the Riemann Zeta function is considered, but nothing more than 10 or 20 pages.


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