Gauss sum
In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically G ( χ ) := G ( χ , ψ ) = ∑ χ ( r ) ⋅ ψ ( r ) {\displaystyle G(\chi ):=G(\chi ,\psi )=\sum \chi (r)\cdot \psi (r)} where the sum is over elements r of some finite commutative ring R, ψ is a group homomorphism of the additive group R+ into the unit circle, and χ is a group homomorphism of the unit group R× into the unit circle, extended to non-unit r, where it takes the value 0. Gauss sums are the analogues for finite fields of the Gamma function.