Ramanujan's sum

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English

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Ramanujan's sum

Noun

Ramanujan 's sum (plural Ramanujan's sums)

(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.

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