CERAMATHS-DMATHS Seminar: Presentation by Abdelmejid Bayad

The CÉRAMATHS Department of Mathematics seminar will host Abdelmejid Bayad (Paris-Saclay University) at 2:00 p.m. on Thursday, June 18, 2026, for the following talk:

Euler-Jordan Functions over Number Fields

Euler’s totient functions $\phi$ and Jordan functions $J_k$ play a central role in number theory, group theory, and the study of congruence rings. In particular, they are involved in counting solutions to Diophantine equations as well as in describing bases of certain modules. Furthermore, they possess subtle arithmetic and analytic properties, which are particularly evident in the study of the means of certain sequences of integers.
As part of ongoing work with Bouchaïb Sodaïgui, we propose to naturally extend this topic to number fields. We will provide an interpretation of these functions in this new setting, present some initial results obtained, and discuss several open problems that arise from them.