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On the connection between the Goldbach conjecture and the Elliott-Halberstam conjecture

In this paper we prove that the binary Goldbach conjecture for sufficiently large even integers would follow under the assumption that both the Elliott-Halberstam conjecture and a variant of the Elliott-Halberstam conjecture twisted by the Möbius function hold, in which the sum of their levels of distribution exceeds 1. This continues the work of Pan in 1982. An analogous result for the twin prime conjecture is obtained by Ram Murty and Vatwani in 2017.

preprint2022arXivOpen access
Jing-Jing HuangHuixi Li
math.NT
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Jing-Jing HuangHuixi Li

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