nLab
Riemann hypothesis

Contents

Idea

The Riemann hypothesis or Riemann conjecture is the famous unproved statement that all nontrivial zeros of the Riemann zeta function are on the vertical line Re(z)=1/2Re(z)=1/2 in the complex plane.

Analogues of the Riemann hypothesis can be considered for many analogues of zeta functions/L-functions. An important case over the finite fields is called the Riemann–Weil conjecture and was proved by Deligne building on earlier ideas of Weil and Grothendieck. Grothendieck however expected a more natural proof using the (hypothetical) theory of motives.

References

Revised on November 21, 2013 13:00:54 by Urs Schreiber (82.169.114.243)