The Riemann Zeta Function in Four Dimensions

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Riemann zeta function is the analytic continuation of the function , where , . The blue curve is a plot of . You can vary using the slider; it acts as the fourth dimension. The black line marks the origin of the - complex plane. The red arrows mark where the zeta function (blue line) crosses the black line (); these are some of the zeros of the zeta function. The so-called trivial zeros appear at negative even integers when . The Riemann conjecture states that the nontrivial zeros all lie on the critical line .

Contributed by: Biswaroop Mukherjee (April 2011)
Open content licensed under CC BY-NC-SA



See an English translation of [1].


[1] B. Riemann, "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse," Monatsberichte der Berliner Akademie in Gesammelte Werke, Teubner, Leipzig 1892.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.