Ramanujan conjecture

proper noun

A conjecture stating that the Ramanujan tau function given by the Fourier coefficients τ(n) of the cusp form Δ(z) of weight 12 Δ(z)=∑_(n>0)τ(n)qⁿ=q∏_(n>0)(1-qⁿ)²⁴=q-24q²+252q³-1472q⁴+4830q⁵-⋯, where q=e^(2πiz), satisfies |τ(p)|≤2p^(11/2), when p is a prime number.

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Meanings

proper nounthe Ramanujan conjecture
  1. mathematicsA conjecture stating that the Ramanujan tau function given by the Fourier coefficients τ(n) of the cusp form Δ(z) of weight 12 Δ(z)=∑_(n>0)τ(n)qⁿ=q∏_(n>0)(1-qⁿ)²⁴=q-24q²+252q³-1472q⁴+4830q⁵-⋯, where q=e^(2πiz), satisfies |τ(p)|≤2p^(11/2), when p is a prime number.

Origin

Named after Srinivasa Ramanujan.

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Cite this entry
APA

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

MLA

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

Chicago

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

Source: Ramanujan conjecture on Wiktionary, CC BY-SA 4.0.