"Ramanujan–Petersson conjecture"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
Pythagoras0 (토론 | 기여) (→메타데이터: 새 문단) |
Pythagoras0 (토론 | 기여) |
||
18번째 줄: | 18번째 줄: | ||
<references /> | <references /> | ||
− | == 메타데이터 == | + | ==메타데이터== |
− | |||
===위키데이터=== | ===위키데이터=== | ||
* ID : [https://www.wikidata.org/wiki/Q630650 Q630650] | * ID : [https://www.wikidata.org/wiki/Q630650 Q630650] | ||
+ | ===Spacy 패턴 목록=== | ||
+ | * [{'LOWER': 'ramanujan'}, {'OP': '*'}, {'LOWER': 'petersson'}, {'LEMMA': 'conjecture'}] | ||
+ | * [{'LOWER': 'ramanujan'}, {'LOWER': "'s"}, {'LEMMA': 'conjecture'}] |
2021년 2월 17일 (수) 00:47 기준 최신판
노트
위키데이터
- ID : Q630650
말뭉치
- 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]
- The Ramanujan–Petersson conjecture for general linear groups implies Selberg's conjecture about eigenvalues of the Laplacian for some discrete groups.[1]
- In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕ m .[2]
- The relationship between roots and coefficients of quadratic equations leads the third relation, called Ramanujan's conjecture.[3]
- 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]
- 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]
- This is what is classically called the Ramanujan-Petersson conjecture.[4]
- Also the latter example can theoretically occur in nature as long as the Ramanujan-Petersson conjecture is not known.[5]
- 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]
- Moreover, a link is established between the assumed distribution of the normalised coefficients and a probabilistic version of the Ramanujan-Petersson Conjecture.[7]
- In particular, this implies that the analogue of the Ramanujan-Petersson conjecture for such forms is essentially the best possible.[8]
소스
- ↑ 1.0 1.1 Ramanujan–Petersson conjecture
- ↑ Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms
- ↑ 3.0 3.1 3.2 Ramanujan–Petersson conjecture
- ↑ Shahidi : On the Ramanujan Conjecture for Quasisplit Groups
- ↑ For what automorphic representations is Ramanujan-Petersson known?
- ↑ Ramanujan Conjecture and the Density Hypothesis
- ↑ On the distribution of coefficients of half-integral weight modular forms and the Ramanujan-Petersson Conjecture
- ↑ Omega Results for Fourier Coefficients of Half-Integral Weight and Siegel Modular Forms
메타데이터
위키데이터
- ID : Q630650
Spacy 패턴 목록
- [{'LOWER': 'ramanujan'}, {'OP': '*'}, {'LOWER': 'petersson'}, {'LEMMA': 'conjecture'}]
- [{'LOWER': 'ramanujan'}, {'LOWER': "'s"}, {'LEMMA': 'conjecture'}]