@article{Kong2025, 
author = {Yafang Kong and Ziyi Song and Lingli Ma and Dengzhe Wang},
title = {The ternary Goldbach problem with primes in arithmetic progressions modulus prime numbers},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {30828-30850},
keywords = {ternary Goldbach problem, prime solutions, arithmetic progressions, circle method, exponential sums},
url = {https://www.sciopen.com/article/10.3934/math.20251353},
doi = {10.3934/math.20251353},
abstract = {In this paper, assuming the Landau's conjecture, we obtained an explicit numerical upper bound for the prime modulus of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result on the quantitative upper bound improved the previous results.}
}