4-22-19. Thomas Craig to H. Poincaré

Nov. 17/86

Athenaeum Club

Franklin & Charles Sts.

Dear M. Poincaré,

If it is not too much trouble for you I wish very much that you would give me information on the following two points.

I. What is the exact meaning of the word “monogène” used by Weierstrass and by Mittag-Leffler in his memoir on uniform functions (Acta Math Vol. IV, I think it is IV but am not sure at this minute).11endnote: 1 Mittag-Leffler (1884). Mittag-Leffler wrote to Poincaré concerning his ongoing research on monogenic functions in September, 1881 (§ 1-1-11). I thought that I knew the meaning of the word in connection with the Theory of Functions, but I do not understand the full significance of it as used by Weierstrass and Mittag-Leffler.

II. Has anything been done on the general Theory of non-uniform functions? If so can you tell me where I can find it?

I shall feel deeply obliged to you if you will be kind enough to answer these questions. I have been much interested in reading your communications and those of M. Picard to the Académie des Sciences in the transformations of surfaces into themselves.22endnote: 2 Poincaré (1886). I have given to my class in Abelian functions your generalization of Abel’s Theorem to gauche curves and to surfaces. I think they got a clearer notion of what the theorem means than they had when I only used a plane curve.

Hoping to hear from you very soon I remain my dear M. Poincaré,

Yours sincerely,

Thomas Craig

ALS 3p. Collection particulière, Paris 75017.

Time-stamp: “ 4.05.2019 00:49”

Notes

  • 1 Mittag-Leffler (1884). Mittag-Leffler wrote to Poincaré concerning his ongoing research on monogenic functions in September, 1881 (§ 1-1-11).
  • 2 Poincaré (1886).

References

  • G. Mittag-Leffler (1884) Sur la représentation analytique des fonctions monogènes uniformes d’une variable indépendante. Acta Mathematica 4, pp. 1–79. Link Cited by: endnote 1.
  • H. Poincaré (1886) Sur les transformations des surfaces en elles-mêmes. Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 103, pp. 732–734. Link Cited by: endnote 2.