Does the Fourier Transform of Ln\zeta(2e^{-s}) Exist?

eljose
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Let be the function Ln\zeta(2e^{-s}) does its Fourier transform exist?...where \zeta(s) is teh Zeta function of Riemann...
 
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In LaTeX the command is \log, ans I presume our latex engine supports this: \log; this this is maths, all logs in mathematics are to base e with the exception of people doing entropy/computing/information theory who use base 2, but would still use log since the usage makes clear that they are in base 2 (no that isn't supposed to start a debate or a flame war, it is a simple observation of the standard notation in higher level maths i.e. NOT what you were told in calc 101).
 
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