Asymptotics of restricted partition functions

Abstract: **NOTE THE UNUSUAL TIME AND DAY**

Given a set $\mathcal A \subset \mathbb N$, the restricted partition function $p_{\mathcal{A}}(n)$ counts the number of integer partitions of $n$ with all parts in $\mathcal A$. In this talk, we will explore the features of the restricted partitions function $p_{\mathbb P_k}(n)$ where $\mathcal P_k$ is the set of $k$-th powers of primes. Powers of primes are both sparse and irregular, which makes $p_{\mathbb P_k}(n)$ quite an elusive function to understand. We will discuss some of the challenges involved in studying restricted partition functions and what is known in the case of primes, $k$-th powers, and $k$-th powers of primes.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

We will email out the link to all registered participants the day before.