Jacobsthal sum explained

In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by .

Definition

The Jacobsthal sum is given by

\phi _{n(a)=\sum} _{m\bmod} \left(\dfrac{m(m ^{n+a)}{p}\right)} where p is prime and is the Legendre symbol