Non-Euclidean Geometry in the Theory of Automorphic Functions (History of Mathematics, V. 17)

This is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincaré. Poincaré's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. The implications of these discoveries continue to be important to this day in numerous different areas of mathematics. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts. This book is the second in an informal sequence of works called "History of Mathematics, Sources", to be included within the History of Mathematics series, co-published by the AMS and the London Mathematical Society. Volumes to be published within this subset are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation on this topic, see Sources of Hyperbolic Geometry, volume 10 in the History of Mathematics series.) Co-published with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.Jacques Hadamard (edited by Jeremy J. Gray and Abe Shenitzer) is the author of 'Non-Euclidean Geometry in the Theory of Automorphic Functions (History of Mathematics, V. 17)', published 1999 under ISBN 9780821820308 and ISBN 0821820303.