The Riemann Hypothesis posits that all non-trivial zeros of the analytically continued Riemann zeta function lie on the critical line where the real part equals one-half within the complex plane. This conjecture establishes a fundamental mechanism linking the distribution of prime numbers to these specific zero locations via an explicit formula involving harmonic terms derived from the zeros' positions. The theory asserts that verifying this condition would provide a rigorous asymptotic bound for the error term in the Prime Number Theorem, thereby precisely predicting prime number density across the natural integers.
The Riemann Hypothesis posits that all non-trivial zeros of the analytically continued Riemann zeta function lie on the critical line where the real part equals one-half within the complex plane. Thi…