# Is this inequality true?

let be the inequality:

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

where [] means modulus of the complex number...

matt grime
b and t are both real and $$\Gamma(x)=\int_0^{\infty}t^{x-1}e^{-t}dt$$
It's certainly not true for any b, remember the asymptotic I gave you for $$\chi$$ 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).