Ramanujan's sum

English

Noun

Ramanujan's sum (plural Ramanujan's sums)

1. (number theory) A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula $c_{q}(n)=\sum _{1\leq a\leq q \atop (a,q)=1}e^{2\pi i{\tfrac {a}{q}}n},$, where (a, q) = 1 means that a only takes on values coprime to q. It is used in the proof of Vinogradov's theorem.