automorphic l-function wikipedia - EAS
- https://en.wikipedia.org/wiki/Automorphic_L-function
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group G of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form. They were introduced by Langlands (1967, 1970, 1971).
Wikipedia · CC-BY-SA 授權下的文字- 預估閱讀時間: 2 分鐘
- https://en.wikipedia.org/wiki/Automorphic_function
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group.
Wikipedia · CC-BY-SA 授權下的文字- 預估閱讀時間: 2 分鐘
- https://en.wikipedia.org/wiki/Automorphic_form
- In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group G {\displaystyle G} acts on a complex-analytic manifold X {\displaystyle X} . Then, G {\displaystyle G} also acts on the space of holomorphic functions from X {\displaystyle X} to the complex numbers. A function f {\displayst...
- 預估閱讀時間: 9 分鐘
- https://en.wikipedia.org/wiki/L-function
- We distinguish at the outset between the L-series, an infinite series representation (for example the Dirichlet series for the Riemann zeta function), and the L-function, the function in the complex plane that is its analytic continuation. The general constructions start with an L-series, defined first as a Dirichlet series, and then by an expansio...
- 預估閱讀時間: 6 分鐘
Automorphic L-function — Wikipedia Republished // WIKI 2
https://wiki2.org/en/Automorphic_L-functionFrom Wikipedia, the free encyclopedia In mathematics , an automorphic L-function is a function L ( s ,π, r ) of a complex variable s , associated to an automorphic representation π of a …
Automorphic function - Encyclopedia of Mathematics
https://encyclopediaofmath.org/wiki/Automorphic_functionAutomorphic function. A meromorphic function of several complex variables that is invariant under some discrete group of transformations Γ of analytic transformations of a given complex …
- https://en.wikipedia.org/wiki/Artin_L-function
One of the aims of proposed non-abelian class field theory is to incorporate the complex-analytic nature of Artin L -functions into a larger framework, such as is provided by automorphic forms …
Automorphic L-function - HandWiki
https://handwiki.org/wiki/Automorphic_L-functionIn mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a …
Ramanujan–Petersson conjecture - Wikipedia
https://en.wikipedia.org/wiki/Ramanujan–Petersson_conjectureIndeed, the L-functions of automorphic forms satisfy the Euler product (1) but they do not satisfy (2) because they do not have the completely multiplicative property. However, Ramanujan …
Automorphic L-function | Detailed Pedia
https://detailedpedia.com/wiki-Automorphic_L-functionIn mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and …
!["Automorphic L-functions and monoids" Ngô Bảo Châu, University of Chicago [2014]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAEALAAAAAABAAEAAAIBTAA7)
