**Ramanujan–Petersson Conjecture**

In mathematics, the **Ramanujan conjecture**, due to Srinivasa Ramanujan (1916, p.176), states that Ramanujan's tau function given by the Fourier coefficients of the cusp form of weight 12

(where *q*=*e*2π*iz*) satisfies

when is a prime number. The **generalized Ramanujan conjecture** or **Ramanujan–Petersson conjecture**, introduced by Petersson (1930), is a generalization to other modular forms or automorphic forms.

Read more about Ramanujan–Petersson Conjecture: Ramanujan Conjecture, Ramanujan–Petersson Conjecture For Modular Forms, Ramanujan–Petersson Conjecture For Automorphic Forms, Applications

### Other articles related to "conjecture":

**Ramanujan–Petersson Conjecture**- Applications

... The most celebrated application of the Ramanujan

**conjecture**is the explicit construction of Ramanujan graphs by Lubotzky, Phillips and Sarnak ...

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