Riemann Zeta Function

The Riemann zeta function, denoted by the Greek letter zeta, is a function of a complex variable defined for real part greater than 1 by the infinite series of reciprocal powers of the positive integers, and extended to the rest of the complex plane, apart from a single pole at 1, by analytic continuation. Leonhard Euler first studied the function for real arguments in the early 1700s, and Bernhard Riemann's 1859 paper extended it to complex variables and established the functional equation connecting its values on either side of the critical strip. The function can also be written as an infinite product over the prime numbers, the Euler product, which ties its behavior directly to the distribution of primes; the Riemann Hypothesis, that every non-trivial zero of the function has real part one half, remains one of the most consequential unsolved problems in mathematics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/