A Rigorous Vanishing-Density Theorem for Modular Collatz Sieves: Explicit Construction and Density Estimates
Year: 2025
Type: article
Abstract: The main result of this work is an explicit construction of a composite modulus M=∏p≤XpM = \prod_{p \le X} pM=∏p≤Xp such that the fraction of residue classes modulo MMM whose Collatz trajectories never reach 1 is arbitrarily small. Consequently, the set of integers that are excluded by all such modular sieves has natural density zero.
Author: RAIL SAKHIULIN
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077069630
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