Automorphic Functions

"Automorphic Functions" provides a comprehensive exploration of the theory and applications of functions that remain invariant under a group of linear transformations. Written by the distinguished mathematician Lester R. Ford, this work delves into the intricate relationship between complex analysis, group theory, and geometry. The text covers fundamental topics such as linear transformations, groups of linear substitutions, and the properties of Fuchsian and Kleinian groups.Through rigorous mathematical proofs and detailed explanations, the volume examines the construction and convergence of series, the theory of conformal mapping, and the analytical properties of automorphic forms. Ford provides a systematic treatment of the subject, building from basic principles to more advanced theorems that serve as a cornerstone for research in number theory and algebraic geometry.This classic mathematical treatise is an essential resource for scholars and students interested in the foundations of complex variables and the development of modern analysis. Its clear exposition and structured approach make it an invaluable reference for understanding the profound connections between various branches of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you may see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. Read more