Unités d'une famille de corps cycliques réels de degré 6 liés à la courbe modulaire \(X_ 1(13)\). (Units of a family of real cyclic fields of degree 6 related to the modular curve \(X_ 1(13))\)
This paper gives a model for the classical modular curve \(X_ 1(13)\) using two functions h and H. The author defines a third function a in terms of h and H and describes modular units. Specializing a to a rational integer, the values of h and H generate a totally real sextic extension K of \({\mathbb{Q}}\). Using all this, the author obtains that in general H-h is a galois generator of the \(unit\quad group\quad of\quad K\quad (mod\quad torsion).\) Finally the paper describes the ramification in K/\({\mathbb{Q}}\).
scientific article; zbMATH DE number 4085763