Ramanujan conjecture

Named after Srinivasa Ramanujan.

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 ${\displaystyle \Delta (z)=\sum _{n>0}\tau (n)q^{n}=q\prod _{n>0}\left(1-q^{n}\right)^{24}=q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}-\cdots ,}$ where ${\displaystyle q=e^{2\pi iz}}$, satisfies ${\displaystyle |\tau (p)|\leq 2p^{11/2},}$ when ${\displaystyle p}$ is a prime number.

• Ramanujan-Petersson conjecture