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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
Tags/Keywords
  • partitions

  • Hardy-Littlewood Circle Method

  • exponential sums

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Partitions Into Polynomial Values

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.

Supplements
27889?type=thumb Gafni Notes 302 KB application/pdf Download
Video/Audio Files

Partitions Into Polynomial Values

H.264 Video 03-Gafni.mp4 79.5 MB video/mp4 rtsp://videos.msri.org/data/000/027/782/original/03-Gafni.mp4 Download
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