Riemann zeta function

The Riemann zeta function, written $\zeta(s)$, begins for suitable complex values of $s$ as the infinite series $\sum_{n=1}^{\infty}n^{-s}$ and is extended more widely by analytic continuation.

Euler's product formula connects it directly with the prime numbers. Its non-trivial zeros are the objects constrained by the Riemann Hypothesis, making the zeta function a central bridge between complex analysis and the distribution of primes.

See also: Euler product, analytic continuation, non-trivial zero, Riemann Hypothesis.

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