Ramanujan–Petersson conjecture

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위키데이터

• ID : Q630650

말뭉치

1. Ramanujan's conjecture implies an estimate that is only slightly weaker for all the \( \tau(n) \), namely \(O(n^{\frac{11}{2}+\varepsilon}) \) for any \(\varepsilon > 0.
2. The Ramanujan–Petersson conjecture for general linear groups implies Selberg's conjecture about eigenvalues of the Laplacian for some discrete groups.
3. In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕ m .
4. The relationship between roots and coefficients of quadratic equations leads the third relation, called Ramanujan's conjecture.
5. Drinfeld's proof of the global Langlands correspondence for GL(2) over a global function field leads towards a proof of the Ramanujan–Petersson conjecture.
6. Another application is that the Ramanujan–Petersson conjecture for the general linear group GL(n) implies Selberg's conjecture about eigenvalues of the Laplacian for some discrete groups.
7. This is what is classically called the Ramanujan-Petersson conjecture.
8. Also the latter example can theoretically occur in nature as long as the Ramanujan-Petersson conjecture is not known.
9. For instance, the Ramanujan-Petersson conjecture for GL(2), proven by Deligne, was a key ingredient in the work of Lubotzky-Phillips-Sarnak on Ramanujan graphs.
10. Moreover, a link is established between the assumed distribution of the normalised coefficients and a probabilistic version of the Ramanujan-Petersson Conjecture.
11. In particular, this implies that the analogue of the Ramanujan-Petersson conjecture for such forms is essentially the best possible.

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위키데이터

• ID : Q630650