6 - Motivating Motives
Indeed the Riemann Hypothesis:
All nontrivial Riemann zeta zeros lie on the line Re(
z
) = 1/2
is equivalent to the claim that $$ | \pi(n) - \mathrm{li}(n) | \le C \sqrt{n} \ln n $$ for some
C
≥ 0 for all
n
≥ 1.
