ramanujan's sum

(number theory) A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula c_q(n)=∑_(1<a≤q atop (a,q)=1)e^(2πi tfrac aqn),, where (a, q) = 1 means that a only takes on values coprime to q. It is used in the proof of Vinogradov's theorem.