Ramanujan conjecture

English

Etymology

Named after Srinivasa Ramanujan.

Proper noun

the Ramanujan conjecture

1. (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