Subgroups of Finite Abelian Groups - Lecture 3

Learn about subgroups of finite Abelian groups in this mathematics lecture from the Combinatorial Methods in Enumerative Algebra program at the International Centre for Theoretical Sciences. Explore how algebraic counting problems generate integer sequences and their relationship to generating functions, with applications to zeta functions and L-functions in number theory. Delve into how Dirichlet's zeta function enumerates ideals of number fields, Witten's zeta function counts Lie group representations, and Hasse-Weil zeta functions encode rational points of algebraic varieties over finite fields. Part of a comprehensive program bringing together experts in zeta functions of groups and rings with combinatorial mathematicians to address outstanding problems in enumerative algebra and train the next generation of researchers in asymptotic group and ring theory.