
Glossary: Prime Pages: Top 5000: 
Riemann noted that his zeta function had trivial zeros
at 2, 4, 6, ... and that all nontrivial zeros were
symmetric about the line Re(s) = 1/2. The
Riemann hypothesis is that all nontrivial zeros are on
this line. In fact the classical proofs of the prime
number theorem require an understanding of the zero free
regions of this function, and in 1901 von Koch showed that
the Riemann hypothesis is equivalent to:
Because of this relationship to the prime number theorem, Riemann's hypothesis is easily one of the most important conjectures in prime number theory.
See Also: RiemannZetaFunction Related pages (outside of this work)
Chris K. Caldwell © 19992017 (all rights reserved)
