Proof of a New Circle Method of Goldbach’s Conjecture

In this paper, a novel circle method is introduced which, compared to previous approaches, eliminates the need to explicitly estimate the prime-variable triangle sum on the residual interval [1]. By employing the Fourier series to express the summation formula, we estimate the triangle sum on the residual interval. At the same time, the concept of the intersection set is introduced. Using this concept, we recalculate the estimated values on both the main and residual intervals, thereby forming a new circle method. This new approach focuses on proving that the main value of the solution count is equivalent to its value on the main interval.