The asymptotic formula in the Goldbach binary problem

TL;DR

This paper solves the Goldbach binary problem using trigonometric sums, deriving an asymptotic formula for the distribution of even numbers as sums of two odd numbers across natural numbers.

Contribution

It introduces a method employing trigonometric sums to establish an asymptotic formula for Goldbach's binary problem.

Findings

Asymptotic formula for even numbers as sums of two odd numbers

Distribution pattern of such sums across natural numbers

Method demonstrates effectiveness in Goldbach's problem

Abstract

The binary problem of Goldbach is solved by the method of the trigonometrical sums. The asymptotic formula of distribution of the even numbers formed by the sum of two simple uneven numbers is found for each even number from the set of natural numbers N.