The critical strip of the Riemann zeta function 
is the region 
, where 
is the real part of the complex number 
. All nontrivial
zeros of 
lie in this open strip.
The Euler product rules out zeros for 
. On the boundary 
, 
has no zeros and has a simple
pole at 
. The functional
equation then rules out zeros for 
apart from the trivial
zeros at the negative even integers (NIST DLMF).
The critical line 
bisects the strip. If 
is a nontrivial zero,
then its complex conjugate 
is also a nontrivial zero.
Applying the functional equation shows that
is another. These are the reflections
of 
across the real axis and the critical
line, respectively. The Riemann hypothesis
asserts that every nontrivial zero lies on the
critical line (NIST DLMF). The quasi-Riemann
hypothesis asserts that the real parts of the nontrivial zeros have a fixed upper
bound strictly less than 1.
