Bhargava's Early Work: The Genesis of P-Orderings
Résumé
As an undergraduate student, Manjul Bhargava gave a full answer to a question on polynomial functions on the integers. He immediately generalized this study to finite principal ideal rings, thanks to the amazingly simple notion of P-ordering. This tool, together with a beautiful generalization of factorials, allowed him to generalize many classical theorems. It turned out to be extremely useful for the study of integer-valued polynomials on subsets.