# On a relaxation of Goldbach's problem

Kam Hung Yau

## Affiliation:

University of New South Wales

## Date:

Tue, 25/06/2019 - 12:00pm to 1:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

The Goldbach conjecture states that all even integer greater than 2 is a sum of two primes. Currently we do not have sufficient tools to prove this conjecture but we can obtain the following relaxation: Uniformly for small $q$ and $(a, q) = 1$, we obtain an estimate for the weighted number of ways a sufficiently large integer can be represented as the sum of a prime congruent to a modulo $q$ and a square-free integer with an even (or odd) number of prime factors. Our method is based on the notion of local model developed by Ramaré and may be viewed as an abstract circle method. I will talk about the history of the problem and the tools surrounding the progress of the conjecture.