Abstract
In this paper we prove that the binary Goldbach conjecture for sufficiently large even integers would follow under the assumptions of both the Elliott-Halberstam conjecture and a variant of the Elliott-Halberstam conjecture twisted by the Möbius function, provided that the sum of their level of distributions exceeds 1. This continues the work of Pan [10]. An analogous result for the twin prime conjecture is obtained by Ram Murty and Vatwani [13].
Dedicated to Professor Melvyn Nathanson on the occasion of his 75th birthday.
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Huang, JJ., Li, H. (2021). On the Connection Between the Goldbach Conjecture and the Elliott-Halberstam Conjecture. In: Nathanson, M.B. (eds) Combinatorial and Additive Number Theory IV. CANT 2020. Springer Proceedings in Mathematics & Statistics, vol 347. Springer, Cham. https://doi.org/10.1007/978-3-030-67996-5_17
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