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number > number theory > analytic number theory > L-function > Ramanujan-Petersson conjecture
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... > topology > differential topology > differentiable manifold > Lie group > automorphic form > Ramanujan-Petersson conjecture
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number > number theory > automorphic form > Ramanujan-Petersson conjecture
... > mathematical analysis > functional analysis > transformation > harmonic analysis > automorphic form > Ramanujan-Petersson conjecture
mathematical analysis > complex analysis > modular form > Ramanujan-Petersson conjecture
number > number theory > analytic number theory > modular form > Ramanujan-Petersson conjecture
... > mathematical analysis > functional analysis > geometry of numbers > arithmetic geometry > modular form > Ramanujan-Petersson conjecture
... > number > number theory > geometry of numbers > arithmetic geometry > modular form > Ramanujan-Petersson conjecture
... > geometry > discrete geometry > geometry of numbers > arithmetic geometry > modular form > Ramanujan-Petersson conjecture
... > number > real number > Diophantine approximation > geometry of numbers > arithmetic geometry > modular form > Ramanujan-Petersson conjecture

Preferred term

Ramanujan-Petersson conjecture  

Definition

  • In mathematics, the Ramanujan conjecture, due to Srinivasa Ramanujan (1916, p. 176), states that Ramanujan's tau function given by the Fourier coefficients τ(n) of the cusp form Δ(z) of weight 12
    where , satisfies
    when p 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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Petersson_conjecture)

Broader concept

Synonym(s)

  • generalized Ramanujan conjecture

In other languages

URI

http://data.loterre.fr/ark:/67375/PSR-Z00WNCP8-4

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