Converse Theorems and L-Functions of Automorphic Forms

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It is proposed to investigate L-functions of automorphic representations and their applications in the following contexts:lifitng from Classical Groups to GL(n);Converse Theorems for GL(n);L-funcitons for GL(n);sub-convexity results for L-functions.These are all ongoing projects. In addition there isa return to previous work on non-symmetric complexhomogeneous domains.The proposal is devoted to the study of Langlans' philosopy,which is the main part of the modern number theory.We obtained, by using Converse Theorem, important resultsrelating the problem of lifting of generic automorphic representations of the classical groups to GL(n).Our basic achivement will be the proof of the local and global Langlands' conjectures.