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math guru's help...purely abstract stuff..

Discussion in 'Random Discussion' started by semidevil, Apr 8, 2004.

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  1. semidevil

    semidevil Thread Starter

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    I'm trying to write a paper on Fermat's Last theorem, and browsing through the web, I found these 2 theorems:

    1. If there is a solution(x, y, z, n) to Fermat's theorem, then the elliptic curve defined by the equation
    Y^2 = X(x - x^n)(X + Y^n) is semistable but not modular

    2. All Semistable elliptic curves w/ rational cofficients are modular.

    My resources from the net gives proofs to the 2 theorems, thereby proving the Fermat problem. but I am having trouble relating the theorems to the Fermat problem. what does it mean for an elliptic curve to be semistable and modualar? I just don't see how it relates.
     
  2. MustBNuts

    MustBNuts

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    Now you know why it was his last theorum! :D:D:D
     
  3. barfly

    barfly

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    I'll leave that one for Albert!
     
  4. AlbertB

    AlbertB

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    Hate to admit defeat but it is easier to just look at the top of this page for the def of modular:
    http://mathworld.wolfram.com/ModularForm.html

    Very good description of the whole shebang here:

    http://mathworld.wolfram.com/Taniyama-ShimuraConjecture.html

    My brain hurts now! :( Too many miles on the clock to remember this stuff, but sadly it comes back too too easily. Frankly I'd rather be Hemmeling! ;)
     
  5. barfly

    barfly

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    Hemmeling :eek:

    I havent heard that in years :D

    is it still on sale?
     
  6. AlbertB

    AlbertB

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  7. AlbertB

    AlbertB

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    I think I really meant "haemorrhaging" Barfly, from the ears! :D
     
  8. semidevil

    semidevil Thread Starter

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    albert,

    thank you so much....for both problems..... I got a 94% on my exam...hehe
     
  9. AlbertB

    AlbertB

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    If that is for what you did yourself under exam conditions then accept my heartiest congratulations Semidevil! A 94%!!!!! Being able to share ideas and get the odd pointer from others is what advancement in any subject is about. Glad to have helped a little. :)

    So have you unified those fields yet then? ;)
     
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