§25.3 Graphics

Notes:: These graphics were constructed at NIST.
Keywords:: Riemann zeta function
Permalink:: http://dlmf.nist.gov/25.3

See accompanying text

Figure 25.3.1: Riemann zeta function $\mathop{\zeta\/}\nolimits\!\left(x\right)$ and its derivative ${\mathop{\zeta\/}\nolimits^{{\prime}}}\!\left(x\right)$ , $-20\leq x\leq 10$ .

Magnify

Symbols:: $\mathop{\zeta\/}\nolimits\!\left(s\right)$ : Riemann zeta function and $x$ : real variable
Permalink:: http://dlmf.nist.gov/25.3.F1
Encodings:: pdf, png

See accompanying text

Figure 25.3.2: Riemann zeta function $\mathop{\zeta\/}\nolimits\!\left(x\right)$ and its derivative ${\mathop{\zeta\/}\nolimits^{{\prime}}}\!\left(x\right)$ , $-12\leq x\leq-2$ .

Magnify

Symbols:: $\mathop{\zeta\/}\nolimits\!\left(s\right)$ : Riemann zeta function and $x$ : real variable
Permalink:: http://dlmf.nist.gov/25.3.F2
Encodings:: pdf, png

See accompanying text

Visualization Help

Figure 25.3.3: Modulus of the Riemann zeta function $|\mathop{\zeta\/}\nolimits\!\left(x+iy\right)|$ , $-4\leq x\leq 4$ , $-10\leq y\leq 40$ .

Magnify

Symbols:: $\mathop{\zeta\/}\nolimits\!\left(s\right)$ : Riemann zeta function and $x$ : real variable
Permalink:: http://dlmf.nist.gov/25.3.F3
Encodings:: VRML, X3D, pdf, png

See accompanying text

Figure 25.3.4: $Z(t)$ , $0\leq t\leq 50$ . $Z(t)$ and $\mathop{\zeta\/}\nolimits\!\left(\tfrac{1}{2}+it\right)$ have the same zeros. See §25.10(i).

Magnify

Symbols:: $\mathop{\zeta\/}\nolimits\!\left(s\right)$ : Riemann zeta function and $Z(t)$ : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F4
Encodings:: pdf, png

See accompanying text

Figure 25.3.5: $Z(t)$ , $1000\leq t\leq 1050$ .

Magnify

Symbols:: $Z(t)$ : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F5
Encodings:: pdf, png

See accompanying text

Figure 25.3.6: $Z(t)$ , $10000\leq t\leq 10050$ .

Magnify

Symbols:: $Z(t)$ : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F6
Encodings:: pdf, png

Choose format for 3D interactive visualization

Please see Visualization Help for details, and Customize to change your choice, or for other customizations.