On an Explicit Construction of a Certain Class of Automorphic Forms
Copyright policy )On an Explicit Construction of a Certain Class of Automorphic Forms
Introduction. In modern terms the problem of construction of autoniorphic functions can be expressed most elegantly in terms of representations of adele groups as the problem of obtaining the explicit spectrum of L2(Gk\GA) where G is an algebraic group defined over a number field k and where GA and G7. are respectively its adele and k-rational points. This space is divided into the space of cusp forms L20(Gk\GA) (with a discrete spectrum) aiid its orthogonal complemeilt. Whereas much is known about the spectrum of the orthogonal complement especially through the work of A. Selberg andc R. P. Langlands on Eisenstein Series, nothing in general is known about the explicit spectrum of the space of cusp forms.
Harmonic analysis on homogeneous spaces, Analysis on other specific Lie groups, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), Other groups and their modular and automorphic forms (several variables), \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Classical groups (algebro-geometric aspects), Representations of Lie and linear algebraic groups over local fields, Automorphic forms in several complex variables
Harmonic analysis on homogeneous spaces, Analysis on other specific Lie groups, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), Other groups and their modular and automorphic forms (several variables), \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Classical groups (algebro-geometric aspects), Representations of Lie and linear algebraic groups over local fields, Automorphic forms in several complex variables
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