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Number Theory Seminar

Partitions into powers of primes

Ayla Gafini, University of Mississippi

Location:  URL: https://us02web.zoom.us/j/386354493?pwd=WEZLaXdSV20vNFpMVVRpb0xXWGhBZz09
Date & time: Tuesday, 14 April 2020 at 2:00PM - 3:00PM

Abstract: 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 \(p_{\mathcal P_k}(n)\) where \(\mathcal P_k\) is the set of \(k\)-th powers of primes.  Powers of primes are both sparse and irregular, which makes \(p_{\mathcal P_k}(n)\) 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.

 

Meeting ID: 386 354 493
Password: 004633

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