Definition
Let p be an odd prime number and a an integer. Then the Gauss sum mod p, g(a;p), is the following sum of the pth roots of unity:
If a is not divisible by p, an alternative expression for the Gauss sum (with the same value) is
Here is the Legendre symbol, which is a quadratic character mod p. An analogous formula with a general character χ in place of the Legendre symbol defines the Gauss sum G(χ).
Read more about this topic: Quadratic Gauss Sum
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