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Graduate Seminar

Zilin Jiang
Carnegie Mellon University
Title: Hardy--Littlewood Circle Method and Waring's Problem

Abstract: Let $A$ be a subset of the natural numbers, and set $r(n; s, A) := $ number of ways to write $n$ as a sum of $s$ elements of $A$. Many important problems can be phrased in terms of these functions. For example, let $A$ be the set of prime numbers. Then Goldbach conjecture is equivalent to $r(n; 2, A) > 0$ for all $n$ even and greater than $2$. The Waring's problem asks for the asymptotics for $r(n; s, A)$, where $A$ is the set of $k$th powers. In this talk, I will try to sketch out some of the major ideas in the Hardy--Littlewood Circle Method in the context of Waring's Problem

Date: Thursday, April 9, 2015
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Zilin Jiang