Frankfurter Seminar – Kolloquium des Instituts für Mathematik

Annette Huber-Klawitter (Universität Freiburg)

Abstract: 1-Periods are complex numbers obtained by integrating an algebraic $1$-form defined over $\mathbf{Q}$ (e.g. $dx/x$) over a chain with algebraic end points. The set contains many interesting numbers (e.g., the values of $\log$ in algebraic numbers). Their transcendence and the relations between them are a classical question of transcendence theory.

We now have complete picture, explaining the relations qualitatively in terms of obvious relations and also quantitatively, by which we mean dimension formulas.

In the talk we are going to explain some of these general results and then discuss the application to the values of the hypergeometric function–recovering results of Wolfart. (joint work with G. Wüstholz)