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Research Article | Open Access

The ternary Goldbach problem with primes in arithmetic progressions modulus prime numbers

Yafang Kong( ), Ziyi Song, Lingli Ma, Dengzhe Wang
School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing Jiaotong University, Chongqing, 400074, China
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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.

Keywords

ternary Goldbach problemprime solutionsarithmetic progressionscircle methodexponential sums
CLC number: 11P32, 11P55

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 30828-30850
DOI: 10.3934/math.20251353

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Cite this article:
Kong Y, Song Z, Ma L, et al. The ternary Goldbach problem with primes in arithmetic progressions modulus prime numbers. AIMS Mathematics, 2025, 10(12): 30828-30850. https://doi.org/10.3934/math.20251353

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Received: 16 June 2025
Revised: 20 December 2025
Accepted: 23 December 2025
Published: 30 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)