zeta function
mathematics
Also known as: Euler zeta function
- Related Topics:
- function
- infinite series
- Riemann zeta function
zeta function, in number theory, an infinite series given by where z and w are complex numbers and the real part of z is greater than zero. For w = 0, the function reduces to the Riemann zeta function, named for the 19th-century German mathematician Bernhard Riemann, whose study of its properties led him to formulate the Riemann hypothesis. The zeta function has a pole, or isolated singularity, at z = 1, where the infinite series diverges to infinity. (A function such as this, which only has isolated singularities, is known as meromorphic.) For z = 1 and w = ...(100 of 152 words)