Hall 123

Circle Method

Manoj Verma

Post Doctoral Fellow, IMSc

Let G(k) denote the smallest natural number s such that every sufficiently
large natural number is a sum of s kth powers of non-negative integers. In
1920s Hardy and Littlewood proved that G(k) <= (k-2)2^(k-1)+5. Combining
their ideas with an inequality proved by Hua in 1938 leads to a proof that
G(k) <= 2^k+1. In this week's talk, we'll see a proof of Hua's lemma and
then finish the treatment of the minor arcs in Waring's problem.
Afterward, we'll start with the treatment of the major arcs.