3. Partitions into Polynomial Values | Ayla Gafni | 2017

Partitions into Polynomial Values

Connections For Women: Analytic Number Theory February 02, 2017 - February 03, 2017

February 02, 2017 (11:45 AM PST - 12:15 PM PST)
Speaker(s): Ayla Gafni (University of Rochester)
Location: MSRI: Simons Auditorium

Abstract
In 1918, Hardy and Ramanujan published a seminal paper which included an asymptotic formula for the partition function. In their paper, they also state without proof an asymptotic equivalence for the number of partitions of a number into k-th powers. In this talk, I will present an asymptotic formula for the number of partitions into k-th powers using a relatively simple method, verifying the claim of Hardy and Ramanujan. We will then discuss extensions of this result to partitions into integer values of polynomials.