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A Greek zeta of a complex variable.
Also known as: Zeta function, Riemann zeta, Zeta
The zeta function sums the reciprocal powers of every positive integer, and its zeros encode the distribution of primes. The Riemann hypothesis — that every non-trivial zero has real part one half — is the most famous unproved statement in mathematics, and the symbol is how it is written.
Denotes the Riemann zeta function, defined by a sum over reciprocal powers and continued analytically to the complex plane.
Contexts: Mathematics
Connects to the primes through its Euler product, which is why its zeros control how the primes are distributed.
Contexts: Mathematics
Is the subject of the Riemann hypothesis, which remains unproved and is one of the Millennium Prize problems.
Contexts: Mathematics
A Greek lowercase zeta — a small hooked stroke descending to a curved tail — followed by a bracketed variable.