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

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SUMMARY

The Fourier Transform of the function Ln\zeta(2e^{-s}), where \zeta(s) represents the Riemann Zeta function, is the central topic of discussion. Participants confirm that the Fourier Transform exists, emphasizing the mathematical properties of logarithms, particularly in relation to base e. The conversation also touches on the notation conventions in higher mathematics, clarifying that logs are typically base e unless specified otherwise. This discussion provides a clear understanding of the mathematical context surrounding the Fourier Transform of logarithmic functions.

PREREQUISITES
  • Understanding of the Riemann Zeta function
  • Familiarity with Fourier Transform concepts
  • Knowledge of logarithmic functions and their properties
  • Basic LaTeX formatting for mathematical expressions
NEXT STEPS
  • Research the properties of the Riemann Zeta function and its applications
  • Study Fourier Transform techniques in mathematical analysis
  • Explore advanced logarithmic functions and their implications in various fields
  • Learn LaTeX for effective representation of mathematical expressions
USEFUL FOR

Mathematicians, theoretical physicists, and students studying advanced calculus or complex analysis who are interested in the properties of the Riemann Zeta function and Fourier analysis.

eljose
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Let be the function [tex]Ln\zeta(2e^{-s})[/tex] does its Fourier transform exist?...where [tex]\zeta(s)[/tex] is the Zeta function of Riemann...
 
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In LaTeX the command is \log, ans I presume our latex engine supports this: [tex]\log[/tex]; 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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