Goldbach Representations of an integer as a Sum of many primes

Abstract: Goldbach’s conjecture states that every even integer greater than two can be written as the sum of two primes. Since this problem is out of reach at the moment, we are interested in the average number of the representations. Asymptotic results for the classical case have been studied intensively to give upper and lower bounds for the error term. Now, we are interested in the number of representations of an integer as a sum of many primes. In this talk, I will present new results in this direction, including: giving upper and lower bounds for the error term, and connections with the Riemann Hypothesis