MathLiveRiemann zeta function
The Riemann zeta function is defined as the infinite series of reciprocal powers of the positive integers, which converges when the real part of z is greater than 1. It is central to number theory, especially the distribution of prime numbers, and is extended to the whole complex plane by analytic continuation.
\zeta(z) = \sum_{n=1}^{\infty} \frac{1}{n^z}, \quad \operatorname{Re} z > 1What the symbols mean
| complex variable, with real part greater than 1 for convergence | |
| positive integer index of summation | |
| real part of the complex number z |
About this formula
- FieldMathematics
- TopicAnalytic number theory
- LevelAdvanced
- Also calledEuler-Riemann zeta function, zeta function, zeta series, zeta(s) series definition
- SourceWikidata Q187235
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