POINCARE, H. (HENRI). - THE DISCOVERY OF AUTOMORPHIC FORMS.

Sur les fonctions fuchsiennes. (+) Sur les fonctions.... Note. (+) Sur les fonctions.... Note.

(Paris: Gauthier-Villars), 1882.

4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences", Vol 94, No 4 + 15 + 17. Pp. (149-) 184, pp. (997--) 1068 a. pp. (1139-) 1214. (3 entire issues offered). Poincare's papers: pp. 163-168, 1038-1042 a. 1166-67.

First appearance in print of the discovery of the automorphic forms, which Poincaré named Fuchsian functions.

"One of Poincaré's first discoveries in mathematics, dating to the 1880s, was automorphic forms. He named them Fuchsian functions, after the mathematician Lazarus Fuchs, because Fuchs was known for being a good teacher and had researched on differential equations and the theory of functions. Poincaré actually developed the concept of these functions as part of his doctoral thesis. Under Poincaré's definition, an automorphic function is one which is analytic in its domain and is invariant under a discrete infinite group of linear fractional transformations. Automorphic functions then generalize both trigonometric and elliptic functions." (Wikipedia).

Order-nr.: 49173