Lecture on Langlands Functoriality Conjecture
نویسنده
چکیده
منابع مشابه
Langlands Functoriality Conjecture
Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which a...
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The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey ...
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In the spirit of the Langlands proposal on Beyond Endoscopy we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions. It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality. Our discussion also includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...
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Three parts of the theory of automorphic forms. I am inclined to divide the modern theory of automorphic forms into three parts: (i) the theory over a number field, F , thus for functions on G(F )\G(AF ); (ii) the theory for functions on G(F )\G(A), where F is the field of rational functions on a Riemann surface, thus closed nonsingular curve, X ; (iii) the relation between automorphic forms in...
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