Patrick’s essay at AIMS undertakes the examination of finite subgroups within the group of homographies, considering coefficients from various types of fields, with a particular focus on the fields of rational, real, and complex coefficients. His exploration began by surveying diverse approaches, drawing inspiration from the works of Gregory Dresden et al. Furthermore, we propose a novel approach based on the periodicity theorem of homographic recurrence by Dorin Andrica and Ovidiu Bagdasar to demonstrate these results. Finally, he presented a new and significant contribution by providing insights into the homographies groups associated with finite sets of rational, including cardinalities of 1, 2, 3, and 4. Additionally, he offered novel findings for sets of cardinality 12n + 7, where n is a non-negative integer.

Currently, Patrick Nyadjo Fonga is pursuing a master’s degree at Sorbonne Paris Nord University in France, focusing on the fascinating field of analytic number theory. His research specifically explores the deep magnitudes exhibited by the Riemann zeta function along the critical line.