The Goldbach Conjecture With Summands In Arithmetic Progressions

: Salmensuu Juho

Publisher: OXFORD UNIV PRESS

: 2022

: Quarterly Journal of Mathematics

: QUARTERLY JOURNAL OF MATHEMATICS

: Q J MATH

: haac008

: 27

: 0033-5606

: 1464-3847

DOI: https://doi.org/10.1093/qmath/haac008

: https://doi.org/10.1093/qmath/haac008

: https://research.utu.fi/converis/portal/detail/Publication/175192603

: https://arxiv.org/abs/2106.00778

We prove that, for almost all r <= N-1/2/log(O(1)) N, for any given b(1) (mod r) with (b(1), r) = 1, and for almost all b(2) (mod r) with (b(2), r) = 1, we have that almost all natural numbers 2(n) <= N with 2n b(1) + b(2) (mod r) can be written as the sum of two prime numbers 2n = p(1) + p(2), where p(1) b(1) (mod r) and p(2) b(2) (mod r) . This improves the previous result which required r <= N-1/3/log(O(1)) N instead of r <= N-1/2/log(O(1))N. We also improve some other results concerning variations of the problem.

haac008.pdf