"Automorphic L-function"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 3번째 줄: | 3번째 줄: | ||
** complex variable $s$, | ** complex variable $s$, | ||
** associated to an automorphic form $\pi$ of a reductive group $G$ over a global field | ** associated to an automorphic form $\pi$ of a reductive group $G$ over a global field | ||
| − | ** a finite-dimensional complex representation $r$ of the Langlands dual group $ | + | ** a finite-dimensional complex representation $r$ of the Langlands dual group $^LG$ of $G$, |
* They were introduced by Langlands (1967, 1970, 1971) | * They were introduced by Langlands (1967, 1970, 1971) | ||
* generalizing the Dirichlet $L$-series of a Dirichlet character and the Mellin transform of a modular form | * generalizing the Dirichlet $L$-series of a Dirichlet character and the Mellin transform of a modular form | ||
2018년 6월 18일 (월) 18:26 판
introduction
- an automorphic L-function is a function $L(s,\pi,r)$
- complex variable $s$,
- associated to an automorphic form $\pi$ of a reductive group $G$ over a global field
- a finite-dimensional complex representation $r$ of the Langlands dual group $^LG$ of $G$,
- They were introduced by Langlands (1967, 1970, 1971)
- generalizing the Dirichlet $L$-series of a Dirichlet character and the Mellin transform of a modular form