How Can You Accurately Draw the Riemann Xi Function Curve?

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SUMMARY

The discussion focuses on accurately drawing the Riemann Xi function curve, specifically the argument Arg\xi(1/2 + iz). It is established that the Riemann Xi function is real for real values of 'z', leading to the conclusion that the argument should equal zero for all real numbers. A specific plotting tool, Wolfram Alpha, is recommended for visualizing the function using the provided formula. The conversation highlights the importance of recognizing the behavior of the function along the x-axis.

PREREQUISITES
  • Understanding of complex analysis, particularly the Riemann Xi function.
  • Familiarity with the Gamma function and its properties.
  • Knowledge of the Riemann Zeta function and its significance in number theory.
  • Basic skills in using online graphing tools like Wolfram Alpha.
NEXT STEPS
  • Research the properties of the Riemann Xi function in detail.
  • Learn how to utilize Wolfram Alpha for complex function plotting.
  • Explore the relationship between the Riemann Zeta function and the Riemann Xi function.
  • Study the implications of the Riemann Hypothesis on complex analysis.
USEFUL FOR

Mathematicians, students of complex analysis, and anyone interested in the graphical representation of complex functions, particularly those studying the Riemann Hypothesis.

zetafunction
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how to draw this curve ??

[tex]Arg\xi (1/2+iz)[/tex]

however i am a bit ashamed because the Riemann Xi function is real for real 'z' so for ALL the real numbers the argument of the [tex]\xi(1/2+iz)[/tex] should be 0 ¡¡
 
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http://www.wolframalpha.com/input/?i=plot+1%2f2(1%2f2%2bI+z)((1%2f2%2bI+z)-1)Gamma((1%2f2%2bI+z)%2f2)%2fPi^((1%2f2%2bI+z)%2f2)Zeta((1%2f2%2bI+z))&incParTime=true

In the graph in the middle you can barely see the hint of the orange horizontal line for the complex part that is lying on the x axis.
 


thanks a lot Bill... :)
 

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