This is the domain coloring of Riemann zeta function. I do get the Re(z) < 1 part of the graph. However I am unsure why the Re(z) > 1 part of the graph is all red with the same brightness and hue. Why is this so?
2026-03-28 03:16:11.1774667771
Domain coloring of Riemann zeta function
701 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in GRAPHING-FUNCTIONS
- Lower bound of bounded functions.
- Do Irrational Conjugates always come in pairs?
- Graph rotation: explanation of equation
- Plot function y = tan(yx)
- Sketching a lemniscate curve with a max function?
- 3 points on a graph
- show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$
- What is this method of sketching a third degree curve?
- Getting a sense of $f(x) = x (\log x)^6$
- Can I describe an arbitrary graph?
Related Questions in RIEMANN-ZETA
- How to find $f(m)=\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^m}\right)^{-1}$ (if $m>1$)?
- Is $e^{u/2}\sum_{n=-\infty}^{\infty}e^{-\pi n^{2}e^{2u}}$ even?
- Explanation of trivial zeros of the Riemann Zeta Function
- How can I prove $\frac{\zeta(k)}{\zeta(k+1)}=\sum\limits_{n=1}^{\infty}\frac{\varphi(n)}{n}\cdot\frac{1}{n^k}$?
- Find the value of $A+B+C$ in the following question?
- Computing the value of a spectral zeta function at zero
- Riemann zeta meromorphic cont. using Abel summation formula
- Show that $\int_0^1\frac{\ln(x)^n}{x-1}dx=(-1)^{n+1}n!\zeta(n+1)$, for $n\geq 1$
- The sum of $\sum_{k=0}^{\infty}\frac{\zeta(2k+2)-1}{{2k+1}}$
- Verify the Riemann Hypothesis for first 1000 zeros.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Just to put my comments into a coherent form and answer:
The way the graph looks like depends on the coloring chosen. For your picture above it was most probably this coloring since your plot is also from wikipedia.
You will notice that the graph of the zeta function in your question is only depicted for values up to 40 on the $x$-axis. The coloring, however, starts changing for slightly bigger values than that only. So, in this domain the whole right side is red. If you plotted the zeta-function for values up to say 150 on the right you would see several differences. I hope this clarifies it.