Ramanujan congruences for partition functions | Department of Mathematics

Ramanujan congruences for partition functions

Event Information
Event Location: 
GAB 461
Event Date: 
Friday, October 27, 2023 - 1:00pm

Integer partitions have been studied by mathematicians for many years and have a wide array of applications in and outside of mathematics. Ramanujan was the first to discover surprising divisibility properties of the classical partition-counting function $p(n)$, known as the Ramanujan congruences. Mathematicians later used the connection between partitions and modular forms to fully classify the Ramanujan congruences for $p(n)$. In this talk, we make use of this connection to conclude something more general about divisibility properties of a special class of modular forms called eta-products, and we explore applications to other types of partition-counting functions.