How Can You Accurately Draw the Riemann Xi Function Curve?

  • Thread starter Thread starter zetafunction
  • Start date Start date
  • Tags Tags
    Curve
zetafunction
Messages
371
Reaction score
0
how to draw this curve ??

Arg\xi (1/2+iz)

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 \xi(1/2+iz) should be 0 ¡¡
 
Physics news on Phys.org


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... :)
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

A The wave vector ##k_\mu## in curved spacetime
Replies
4
Views
1K
I A concise "proof" of the Riemann-Lebesgue lemma
Replies
1
Views
1K
I Characteristic curves for ##u_t + (1-2u)u_x = -1/4, u(x,0) = f(x)##
Replies
2
Views
3K
I How to Show \(\psi_{i}\ket{\xi} = \xi_{i}\ket{\xi}\)?
Replies
4
Views
1K
How Do Killing Vector Fields Form a Basis on S2?
Replies
0
Views
1K
A Anti-dual numbers and what are their properties?
Replies
1
Views
2K
A proposed Hamiltonian operator for Riemann Hypothesis
Replies
32
Views
9K
I A thought about the Riemann hypothesis
Replies
7
Views
2K
I Understanding Frequency in Rindler Coordinates for a Scalar Massless Field
Replies
2
Views
1K
How to solve this 2nd order ODE?
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top