I was reading Goldbach problem(Ternary version) and encountered the Hardy-Littlewood circle method.In this method,we work with a number $r(n)=\sum\limits_{n=n_1+n_2+n_3}\Lambda(n_1)\Lambda(n_2)\Lambda(n_3)$ where $\Lambda$ is the Von Mangoldt function.I want to know why we are working with such an expression.What is the underlying idea that motivated us to work with this quantity?
2026-03-25 14:37:38.1774449458
Why is the function $r(n)$ of particular interest in Circle method?
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