Riemann zeta function
In mathematics, the Riemann zeta function, is a prominent function of great significance in number theory. It is named after German mathematician Bernhard Riemann. It is so important because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics.
When using mathematical symbols to describe the Riemann zeta function, instead of explaining it using English, it is explained like this:
s must be a complex number, meaning that it involves the square root of -1
However, because this doesn't work for numbers where R(s)<1, Riemann used some very clever mathematics known as analytic continuation, so that it would work for every number except 1 (where the function just gives you infinity).
Leonhard Euler discovered the first results about this function in the eighteenth century. It is named after Bernhard Riemann, who wrote about it in the memoir "On the Number of Primes Less Than a Given Magnitude", published in 1859.
The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function. Many mathematicians consider the Riemann hypothesis to be the most important unsolved problem in pure mathematics. 
References[change | change source]
- Bombieri, Enrico. "The Riemann Hypothesis - official problem description". Clay Mathematics Institute. http://www.claymath.org/millennium/Riemann_Hypothesis/riemann.pdf. Retrieved 2008-10-25.
- Riemann, Bernhard|http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf%7Ctitle=On the Number of Prime Numbers less than a Given Quantity|