16 octobre 2020
Trigonometric functions and modular symbols
16 octobre 2020 de 15 h 00 à 16 h 00 (heure de Montréal/HNE) Réunion Zoom
Colloque par Nicolas Bergeron (École normale supérieure (Paris), France)
Conférence de la Chaire Aisenstadt
Semestre thématique : Théorie des nombres - Cohomologie en arithmétique
In his fantastic book “Elliptic functions according to Eisenstein and Kronecker”, Weil writes:
“As Eisenstein shows, his method for constructing elliptic functions applies beautifully to the simpler case of the trigonometric functions. Moreover, this case provides […] the simplest proofs for a series of results, originally discovered by Euler.”
The results Weil alludes to are relations between product of trigonometric functions. I will first explain how these relations are quite surprisingly governed by relations between modular symbols (whose elementary theory I will sketch). I will then show how this story fits into a wider picture that relates the topological world of group homology of some linear groups to the algebraic world of trigonometric and elliptic functions. To conclude I will briefly describe a number theoretical application.
This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh.