Ramanujan–Petersson Conjecture

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=eiz) 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 ConjectureRamanujan 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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