Ramanujan conjecture

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English

English Wikipedia has an article on:

Ramanujan conjecture

Etymology

Named after Srinivasa Ramanujan.

Proper noun

the Ramanujan conjecture

(mathematics) A conjecture stating that the Ramanujan tau function given by the Fourier coefficients $τ (n)$ of the cusp form $Δ(z)$ of weight $12$ $\Delta (z)=\sum _{n>0}\tau (n)q^{n}=q\prod _{n>0}\left(1-q^{n}\right)^{24}=q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}-\cdots ,$ where $q=e^{2\pi iz}$ , satisfies $|\tau (p)|\leq 2p^{11/2},$ when $p$ is a prime number.

Related terms

Ramanujan-Petersson conjecture

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