Kloosterman Sum

In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let a, b, m be natural numbers. Then

Here x* is the inverse of x modulo m. They are named for the Dutch mathematician Hendrik Kloosterman, who introduced them in 1926 when he adapted the Hardy-Littlewood circle method to tackle a problem involving positive definite diagonal quadratic forms in four as opposed to five or more variables, which he had dealt with in his dissertation in 1924.