Trois suppléments sur la découverte des fonctions fuchsiennes; Three Supplementary Essays on the Discovery of Fuchsian Functions

1997

hp1997tsa

fr

The three suppléments by Poincaré, written in 1880, are published here for the first time. They document his discovery of automorphic functions and the important role non-Euclidean geometry can play in complex function theory. They precede his published papers of 1881 on the subject, and they show in detail how he made and exploited a succession of insights into what was to become his first major contribution to mathematics. To assist in the understanding of these papers we first indicate something of Poincaré’s life at the time, and describe the context in which he was working. Then we summarize and analyze the mathematical content of the suppléments, focusing on what is new and significant in what he did. We indicate also how these discoveries made their way into the many papers that Poincaré was to publish on this subject. Lastly, we indicate briefly how these suppléments came to be rediscovered, and conjecture how they were lost.

Forme automorphe