Generalization of Goldbach’s ternary problem with almost equal terms

An asymptotic formula is obtained for the number of representations of a sufficiently large natural 𝑁 in the form 𝑏_1𝑝_1 + 𝑏_2𝑝_2 + 𝑏_3𝑝_3 = 𝑁 with the conditions $$ |𝑏_𝑖 𝑝_𝑖 - N/3|⩽ 𝐻, 𝐻 ⩾ (𝑏_1*𝑏_2*𝑏_3)^(4/3)𝑁^2/3)(ln𝑁)&60, 𝑏_𝑖 ⩽ (ln𝑁)^(𝐵_𝑖), $$ where 𝑏_1, 𝑏_2, 𝑏_3, 𝑁 are pairwise coprime natural numbers, 𝐵_𝑖 — arbitrary fixed positive numbers

Перевод пока недоступен