Abstract: |
Note: This is a (blackboard) talk for a general audience.
Abstract: The first systematic study of the number of prime
factors was due to Hardy and Ramanujan in 1917. This eventually
gave rise to probabilistic number theory with the work of
Turan, and Erd\"os-Kac. We will provide a selection of beautiful
classical results on the number of prime factors and discuss
many newer results for which restrictions are placed on
the sizes of the prime factors. These lead to surprising twists
of the classical theme.
Note by P. Paule: Professor Alladi is a leading expert in number
theory, combinatorics, partitions, and q-series identities. He is
founder and editor-in-chief of the highly successful Ramanujan
Journal.
Note by P. Paule: Professor Alladi is a leading expert in number theory,
combinatorics, partitions, and q-series identities. He is founder and
editor-in-chief of the highly successful Ramanujan Journal. |