Automorphic spectral identities and applications to automorphic L -functions onGL2
نویسندگان
چکیده
منابع مشابه
Automorphic 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...
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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...
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PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...
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Our goal is to formulate a theorem that is part of a recent classification of automorphic representations of orthogonal and symplectic groups. To place it in perspective, we devote much of the paper to a historical introduction to the Langlands program. In our attempt to make the article accessible to a general mathematical audience, we have centred it around the theory of L-functions, and its ...
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on Γ\H, parametrized as λw = w(w−1). Haas listed the w-values. Haas thought he was solving the differential equation (∆ − λ)u = 0. Stark and Hejhal observed zeros of ζ and of an L-function on Haas’ list. This suggested an approach to proving the Riemann Hypothesis, since it seemed that zeros w of ζ might give eigenvalues λ = w(w − 1) of ∆. Since ∆ is a self-adjoint, nonpositive operator, these ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2012.05.028