## Riemann zeta function
One of the most profound and mysterious objects in modern mathematics; from it has sprung the Riemann hypothesis and all that this conjecture seems to imply. The Riemann zeta function is closely tied to the distribution of prime numbers. It is an extension of the Euler zeta function,
first studied by Leonhard Euler, which is
the sum Euler found that this function is linked to the occurrence of prime numbers by the following fundamental relationship: s) = 1 + 1/2s + 1/3s + 1/4s
+ ... = 2n/(2n - 1) × 3n/(3n
- 1) × 5n/(5n - 1) × 7n/(7n
- 1) × ...
The Riemann zeta function extends the definition of Euler's zeta function to all complex numbers. ## Related category• NUMBER THEORY | ||||||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |