Riemann Hypothesis

Establish whether all nontrivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2.

Background

The paper reviews classical facts about the Riemann zeta function, emphasizing the central open question known as the Riemann Hypothesis, which asserts that all nontrivial zeros of ζ(s) lie on the critical line Re(s)=1/2. This conjecture is foundational in analytic number theory due to its deep implications for the distribution of prime numbers.

Within the context of the paper, the Riemann Hypothesis is introduced as motivation for studying PDE flows driven by ζ(s) and related Dirichlet L-functions; the authors note its longstanding unresolved status.