By Salahoddin Shokranian

This booklet in line with lectures given by way of James Arthur discusses the hint formulation of Selberg and Arthur. The emphasis is laid on Arthur's hint formulation for GL(r), with numerous examples which will illustrate the fundamental strategies. The booklet can be necessary and stimulating examining for graduate scholars in automorphic types, analytic quantity conception, and non-commutative harmonic research, in addition to researchers in those fields. Contents: I. quantity conception and Automorphic Representations.1.1. a few difficulties in classical quantity idea, 1.2. Modular varieties and automorphic representations; II. Selberg's hint formulation 2.1. historic feedback, 2.2. Orbital integrals and Selberg's hint formulation, 2.3.Three examples, 2.4. an important , 2.5. Generalizations and purposes; III. Kernel features and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and aid conception, 3.3. The convergence theorem; IV. The advert lic thought, 4.1. easy evidence; V. The Geometric idea, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. the load services; VI. The Geometric Expansionof the hint formulation, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral concept, 7.1. A evaluation of the Eisenstein sequence, 7.2. Cusp types, truncation, the hint formulation; VIII.The Invariant hint formulation and its purposes, 8.1. The invariant hint formulation for GL(r), 8.2. purposes and comments