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.
Read more about Kloosterman Sum: Context, Properties of The Kloosterman Sums, Estimates, Short Kloosterman Sums, Lifting of Kloosterman Sums, Kuznetsov Trace Formula, History
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