# nLab Riemann hypothesis

### Context

#### Higher algebra

higher algebra

universal algebra

# 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 $\mathrm{Re}\left(z\right)=1/2$ 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)