Year: 2025
Type: preprint
Abstract: We study small gaps between Goldbach primes $\mathbb{P} \cap (N-\mathbb{P})$ using the Bombieri-Davenport method and the Maynard-Tao method, and compare the two. We show that for almost all even integers $N$, the smallest gap in $\mathbb{P} \cap (N-\mathbb{P})$ is at most $0.765\ldots$ times the average gap, using the Bombieri-Davenport method. This improves a recent result of Tsuda. We also demonstrate that a straightforward application of the Maynard-Tao method is insufficient to improve this bound. However, it allows us to establish the existence of bounded gaps between Goldbach primes with bounded error for almost all even integers $N$.
Source: arXiv (Cornell University)
Author: Akeno, Mizuki
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416934742
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