An Introduction To The Theory Of Automorphic Functions Classic Reprint

An Introduction to the Theory of Automorphic Functions (Classic Reprint)

Excerpt from An Introduction to the Theory of Automorphic Functions Owing largely to the researches of Poincare and Klein the domain of Automorphic Functions has expanded enormously during the last thirty-five years; and the ramifications of the subject have extended into many and diverse fields. This has caused embarrassment in the selection of materials for a book of modest dimensions, and has necessitated a brief treatment, or in some cases the exclusion, of many important and attractive subjects. The aim throughout has been to present in as thorough a manner as possible the concepts and theorems on which the theory is founded, and to describe in less detail certain of its important developments. The present tract had its origin in a series of lectures on Automorphic Functions given to the Mathematical Research Class of the University of Edinburgh during the Spring Term of 1915. I wish to express a grateful acknowledgment of my indebtedness to Professor Whittaker, who has read the manuscript during the course of its preparation, and has made many valuable suggestions; and to Mr Herbert Bell, who has assisted in the preparation of the Bibliography. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

An Introduction to the Langlands Program

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapters of this monograph present a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Covered are a variety of areas in number theory from the classical zeta function up to the Langlands program. The exposition is sytematic, with each chapter focusing on a particular topic devoted to special cases of the program, and accessible to graduate students and researchers in the field.

Spectral Theory of Automorphic Functions