Year: 2026
Type: preprint
Abstract: Let $5\leq p_1<\cdots0$. Maximizing this bound over squarefree moduli whose prime factors do not exceed a prime $p$ gives an explicit threshold $\mathcal N(p)$ satisfying $\log\mathcal N(p)\sim(\log3)p/\log p$. We also describe the complete prime cutoff at $\sqrt{2n}$ and its exact additive-prime interpretation. We also evaluate $g_P(2tP)$ explicitly using the real character of period $3$. The positivity thresholds are elementary and fully explicit; lower-bound sieves provide smaller asymptotic scales, and the present thresholds do not establish positivity at the complete cutoff for all $n\geq13$.
Source: arXiv (Cornell University)
Author: Salazar, Andres M.
Institution: Pontificia Universidad Javeriana
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214129278