Ramanujan's sum

noun

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.

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounRamanujan's sum (plural Ramanujan's sums)

plural Ramanujan's sums

  1. mathematicsA 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.
Cite this entry
APA

Ramanujan's sum. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Ramanujan's%20sum

MLA

“Ramanujan's sum.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Ramanujan's%20sum. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Ramanujan's sum,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Ramanujan's%20sum.

Source: Ramanujan's sum on Wiktionary, CC BY-SA 4.0.