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Spectral interpretation of Primes

  1. Jun 21, 2009 #1
    the idea is

    is there a Linear operator L so [tex] L | \phi _n > =p_n |\phi_n > [/tex]

    with p_n being the nth prime and L a linear operator , is it possible to have an spectral interpretation for prime numbers ?
  2. jcsd
  3. Jun 21, 2009 #2
    I don't think your formula makes sense, but I am not sure. It looks like you have L and p(n)each divide [tex]\phi_n[/tex] but should that really be so since [tex]\phi_n[/tex] should be less than p(n)?
    PS There are over 20,000 articles in science direct that combined the words spectral and primes. Some mention a spectral analysis of the prime intevals etc., but I dont have access to the specific articles.
    Last edited: Jun 21, 2009
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