The function is denoted by the symbol ζ(s), where s is a complex number. It is defined for all values of s except for s = 1, where it is undefined. The Riemann Zeta Function can be expressed as an infinite sum:ζ(s) = 1 + 1/2^s + 1/3^s + 1/4^s + ...Each term in the sum is a fraction with a denominator that is a power of a natural number, raised to the power of s. When s is a positive even integer, the sum can be calculated exactly, but for other values of s, the sum diverges and cannot be calculated exactly.

One of the most interesting properties of the Riemann Zeta Function is that it has a connection to the distribution of prime numbers. In particular, Riemann showed that the zeros of the function are related to the distribution of primes. The zeros of the function occur when certain complex values of s make the sum equal to zero. The first few zeros of the function are located on the critical line where the real part of s is equal to 1/2.

The Riemann Hypothesis is a famous unsolved problem in mathematics that concerns the zeros of the Riemann Zeta Function. It states that all non-trivial zeros of the function lie on the critical line. This hypothesis has far-reaching implications for the distribution of prime numbers and has been the subject of much research for over a century.