Automorphic forms, representations and L-functions
نویسندگان
چکیده
منابع مشابه
L-Functions and Automorphic Representations*
There are two kinds of L-functions, and they will be described below: motivic L-functions which generalize the Artin L-functions and are defined purely arithmetically, and automorphic L-functions, defined by data which are largely transcendental. Within the automorphic L-functions a special class can be singled out, the class of standard L-functions, which generalize the Hecke L-functions and f...
متن کاملAutomorphic Representations and L-functions
• Decomposition by central characters • Square-integrable cuspforms • Smoothness of cuspforms • Eigen-cuspforms and automorphic representation • Dirichlet series versus zeta and L-functions • L-functions defined via local data • Factoring unitary representations of adele groups • Spherical representations and Satake parameters • Local data, L-groups, higher L-functions References and historical...
متن کاملLanglands picture of automorphic forms and L - functions
Recall the lectures in the first two weeks. We discussed Tate’s thesis, i.e. automorphic forms of GL1, which is a generalization of Hecke’s work in 1910’s. Now suppose f ∈ Sk(Γ) is an Hecke eigenform with normalized 1-st Fourier coefficient a1 = 1. Ramanujan-Deligne theorem says ∣∣a(p)p− k−1 2 ∣∣ 6 2, for any p. Let cp = a(p)p− k−1 2 = αp + α−1 p . The Dirichlet series associated f , which is n...
متن کاملWeek 1: Automorphic Forms and Representations
Brief introduction to cyclotomic theory over Q using adeles. Discussion of the definitions of modular forms and automorphic forms. Introducing the adelic automorphic forms via strong approximation theorem. Discussion of the connected components of Shimura varieties (modular curves). Smooth/admissible representations of locally finite groups. Definition and admissibility of (cuspidal) automorphi...
متن کاملAutomorphic forms and - adic representations 4
In Carayol’s note [4], a geometric construction of the Galois representations associated to Hilbert modular forms and the compatibility with the local Langlands correspondence are discussed. In loc. cit., the compatibility is established in the case = p where the Galois representation is an -adic representation and p is the prime divided by the prime p of the totally real field where the restri...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1983
ISSN: 0001-8708
DOI: 10.1016/0001-8708(83)90017-8