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Let $f$ be a holomorphic function in the unit disk of the complex planevfixing the origin with di erential of modulus 1. The local inversion theorem guarantees that f admits a holomorphic inverse g in a small disk of radius $r>0$ centered at the origin. Andre Bloch showed that the maximum radius of existence of g is bounded below by an absolute constant $b>1/72$.

This is Andre Bloch most famous theorem, which has been published in 1925 in the Annales de la Faculte des Sciences Toulouse. The optimal absolute constant b is still unknown today, despite numerous works and steady progress (see e.g. Bonk, M. ; Eremenko, A. ; Covering properties of meromorphic functions, negative curvature and spherical geometry. Ann. of Math. (2) 152 (2000), no. 2, 551-592).
Andre Bloch was an unusual mathematician. You'll nd some biographical information in this article by H. Cartan and J. Ferrand.

The Annales de la Faculté des Sciences de Toulouse was founded in 1887 by Andoyer, Baillaud, Berson, Chauvin, Cosserat, Destrem, Fabre, Legoux, Sabatier and Stieltjes. This multidisciplinary journal has been exclusively dedicated to mathematics since 1979. It publish high level articles and surveys, written in French or in English, in all areas of mathematics. There is no size restriction.

The Annales de la Faculté des Sciences de Toulouse has been a Diamond open access journal since 2017. It is published with the support of CNRS, Université Paul Sabatier and  the Institut de Mathématiques de Toulouse.


This journal, previously hosted by Cedram, is now web-published by the Centre Mersenne. In 2019, Cedram has become the Centre Mersenne for open scientific publishing, a publishing platform for scientific journals developed by Mathdoc.