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Weierstrass theorems and primes.

  1. Apr 9, 2007 #1

    tpm

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    Does 'Weirstrass theorem' allow the existence of an entire function so:

    [tex] f(z)= g(z) \prod _p(1- \frac{x}{p^{k}}) [/tex]

    so for every prime p then f(p)=0 , and k>1 and integer??

    the main question is to see if a function can have all the primes as its real roots
     
    Last edited: Apr 9, 2007
  2. jcsd
  3. Apr 9, 2007 #2

    matt grime

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    Of course a function can have the primes, and only the primes, as its only roots, although you clearly want the function to be analytic, don't you, eljose?
     
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