"Ramanujan–Petersson conjecture"의 두 판 사이의 차이

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== 메타데이터 ==
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==메타데이터==
 
 
 
===위키데이터===
 
===위키데이터===
 
* ID :  [https://www.wikidata.org/wiki/Q630650 Q630650]
 
* ID :  [https://www.wikidata.org/wiki/Q630650 Q630650]
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===Spacy 패턴 목록===
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* [{'LOWER': 'ramanujan'}, {'OP': '*'}, {'LOWER': 'petersson'}, {'LEMMA': 'conjecture'}]
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* [{'LOWER': 'ramanujan'}, {'LOWER': "'s"}, {'LEMMA': 'conjecture'}]

2021년 2월 17일 (수) 00:47 기준 최신판

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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.[1]
  2. The Ramanujan–Petersson conjecture for general linear groups implies Selberg's conjecture about eigenvalues of the Laplacian for some discrete groups.[1]
  3. In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕ m .[2]
  4. The relationship between roots and coefficients of quadratic equations leads the third relation, called Ramanujan's conjecture.[3]
  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.[3]
  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.[3]
  7. This is what is classically called the Ramanujan-Petersson conjecture.[4]
  8. Also the latter example can theoretically occur in nature as long as the Ramanujan-Petersson conjecture is not known.[5]
  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.[6]
  10. Moreover, a link is established between the assumed distribution of the normalised coefficients and a probabilistic version of the Ramanujan-Petersson Conjecture.[7]
  11. In particular, this implies that the analogue of the Ramanujan-Petersson conjecture for such forms is essentially the best possible.[8]

소스

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Spacy 패턴 목록

  • [{'LOWER': 'ramanujan'}, {'OP': '*'}, {'LOWER': 'petersson'}, {'LEMMA': 'conjecture'}]
  • [{'LOWER': 'ramanujan'}, {'LOWER': "'s"}, {'LEMMA': 'conjecture'}]