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Is this inequality true?

  1. Aug 15, 2005 #1
    let be the inequality:

    [tex][\frac{\Gamma(1/4-b/2-it/2)}{\Gamma(1/4+b/2+it/2)}]<\frac{\Gamma(1/4-b/2)}{\Gamma(1/4+b/2)} [/tex]

    where [] means modulus of the complex number...
  2. jcsd
  3. Aug 15, 2005 #2

    matt grime

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    and gamma is the gamma function presumably... is b any real or complex number? and t? apparently b must be real, looking at it. i mean, is the rhs modded too?
  4. Aug 15, 2005 #3
    b and t are both real and [tex]\Gamma(x)=\int_0^{\infty}t^{x-1}e^{-t}dt [/tex]
    Last edited: Aug 15, 2005
  5. Aug 16, 2005 #4


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    It's certainly not true for any b, remember the asymptotic I gave you for [tex]\chi[/tex] before? It can easily tell you which b's even have a chance for this to be true and also that for these b's it will hold for a large enough |t| (though not uniformly).
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