AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (277.6 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 30828-30850
DOI: 10.3934/math.20251353

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

798

Views

7

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)