Langlands fonktörsellik ilkesi

In this thesis we aimed to study functoriality principle of Langlands which is an important part of the Langlands programme, regarded as the grand unified theory connecting number theory and harmonic analysis. With the introduction, this thesis consists of eight chapters. In the first chapter, we studied basics of local and global abelian class field theories in which one can see Langlands conjectures as non-abelian versions of these two theories. In the second chapter we investigated Weil groups and Weil-Deligne representations which are generalizations of Galois groups and Galois representations in various important cases. In particular their relation with l-adic Galois representations are investigated. In the third and fourth chapter, we studied basic theory of algebraic groups and automorphic representations both archimedean and non-archimedean setting which constitutes primary objects to state Langlands conjectures. Their relation with Lie algebras and root systems are investigated. Also Hecke algebras associated to locally profinite groups studied and Flath's decomposition theorem is proved. In the fifth and sixth chapter, L-groups of Langlands associated to connected reductive groups constructed and L-homomorphism between them are defined. L-functions and epsilon-factors associated to Weil-Deligne and automorphic representations are studied. We defined automorphic L-functions and studied the Langlands-Shahidi method with the basic theory of Eisenstein series. In the seventh chapter, local and global functoriality principle of Langlands are stated. The automorphic Langlands group of a global field defined and its excepted properties are stated. Last but not least, some examples of functoriality principle provided.