Major arcs for Goldbach's theorem

H. A. Helfgott (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer N greater than 5 is the sum of three primes. The present paper proves this conjecture. Both the ternary Goldbach conjecture and the binary, or strong, Goldbach conjecture had their origin in an exchange of letters between Euler and Goldbach in 1742. We will follow an approach based on the circle method, the large sieve and exponential sums, supplemented by rigorous computations, including a verification of zeros of L-functions due to D. Platt. The improved estimates on exponential sums are proven in a twin paper by the author.

Domaines: Théorie des nombres [math.NT]

H. A. Helfgott. Major arcs for Goldbach's theorem. 2013. ⟨hal-00827999⟩