What does ramanujan's sum mean?

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.

Word Pronunciation & Dictionary

ramanujan's sum

Word Rarity Very rare

Frequency: Zipf frequency 1.02 in modern English

Syllables: ra-manu-jan's -sum
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Meaning

noun

A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula c_q(n)=∑_(1atop (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.

Inflected Forms

Ramanujan's sums (plural)

Questions

What does ramanujan's sum mean?: A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula c_q(n)=∑_(1atop (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.

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