Exploring the Realness of the Riemann Xi Function: Drawing the Curve

  • Thread starter zetafunction
  • Start date
  • Tags
    Curve
In summary, The conversation discusses how to draw a curve for the Riemann Xi function with a real argument and provides a link to a graph showing the curve and a horizontal line representing the complex part on the x axis.
  • #1
zetafunction
391
0
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 ¡¡
 
Physics news on Phys.org
  • #2


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.
 
  • #3


thanks a lot Bill... :)
 

1. How do I draw a curve?

To draw a curve, start by choosing a point on a graph and plotting it. Then, choose another point and draw a line connecting the two. Continue this process until you have several points plotted on the graph. Finally, use a smooth, curved line to connect the points to create the curve.

2. What is the equation for a curve?

The equation for a curve can vary depending on the type of curve being drawn. Some common equations for curves include quadratic equations, cubic equations, and trigonometric equations. It is important to determine the type of curve you are trying to draw in order to find the appropriate equation.

3. How do I make a curved line look smooth?

To make a curved line look smooth, it is important to use a sufficient number of points when plotting the curve. The more points you have, the smoother the curve will appear. Additionally, using a curved ruler or tracing around a circular object can help you create a smoother, more precise curve.

4. Can I draw a curve without using a graph?

Yes, it is possible to draw a curve without using a graph. You can use a curved ruler or tracing around a circular object to create a smooth curve. However, using a graph can help you create a more accurate and precise curve.

5. How do I know which points to plot for a curve?

The points to plot for a curve will depend on the equation or function being used. You can use a calculator or graphing software to plot the points, or you can use a table of values and plot the points manually. It may also be helpful to consult a graphing guide or textbook for specific equations and their corresponding points.

Similar threads

Replies
2
Views
986
  • Advanced Physics Homework Help
Replies
0
Views
501
  • Linear and Abstract Algebra
Replies
1
Views
862
  • MATLAB, Maple, Mathematica, LaTeX
Replies
9
Views
2K
  • General Math
Replies
7
Views
1K
Replies
2
Views
829
  • Calculus and Beyond Homework Help
Replies
14
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
21
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
665
Back
Top