Sums of powers of almost equal primes
Speaker:
Angel Kumchev, Towson University
Date and Time:
Friday, March 17, 2017 - 9:30am to 10:00am
Location:
Fields Institute, Room 230
Abstract:
I will review some recent results on the Waring-Goldbach problem with almost equal summands. Let $k \ge 2$ and $s$ be positive integers, and let $n$ be a large positive integer subject to certain local conditions. Work by Wei and Wooley and by Huang established that if $s \ge k^2+k+1$ and $\theta > 19/24$, then $n$ can be expressed as a sum $p_1^k + \cdots + p_s^k$, where $p_1, \dots, p_s$ are primes with $|p_j - (n/s)^{1/k}| \le n^{\theta/k}$. In a recent joint work with Huafeng Liu, we extend the range of $\theta$ in this result to $\theta > 31/40$. I will outline the main ideas involved in the proofs of these theorems.