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Please recommend books

  1. Feb 28, 2012 #1
    i am interested in Riemann zeta function. i am in a high school.
    i have good hold over calculus(at least what's required for physics).
    Would Tom Apostle's Calculus I be good to further improve my skills.

    What should i do next?
    Real Analysis or Complex Analysis or directly analytic number theory?

    Are L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle good at my level?

    By the way, has Riemann hypothesis been proved?
    have a look at http://www.coolissues.com/mathematics/Zeta/zeta.htm.

    There are several pages by same author, on several unsolved problems,here:
    http://www.coolissues.com/mathematics/Zeta/zeta.htm
     
  2. jcsd
  3. Feb 28, 2012 #2
    Real analysis first, then complex analysis, then basic number theory, then analytic number theory. And a strong grounding in multivariable calculus will help a lot with complex variables, so don't skip that.

    If you're interested in analytic number theory, there's a book you can start reading right now and grow into as you learn more. Hardy and Wright. It's a classic.

    https://www.amazon.com/Introduction-Theory-Numbers-G-Hardy/dp/0199219869
     
  4. Feb 29, 2012 #3
    Hi sparsh12, I wish you all the best in your mathematical endeavors.

    Just want to mention that the links you included are by a mathematical crank. There are lots of them out there, doing their own "research", and producing results, that if true, would cause well establish facts to be wrong. James Constant is a quite sophisticated crank, he knows a fair amount of math, he can write coherently, but his conclusions are just wrong. When a crank gets a result that contradicts hundreds of years of work by the best minds on the planet, they do not pause and ponder "where did I go wrong?", instead they have an urge to inform us all about their discoveries. I Just remembered that cranky stuff isnt allowed here in the forum, so I should stop.
     
  5. Feb 29, 2012 #4
    There is a lot of valid info on the net as well as invalid info.

    Keep learning and reading. So far no proof of RH that I know of exists.
     
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