A note on variants of Buchstab's identity

2025/03/26 by Runbo Li, Li, Runbo
Mathematics · #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.07974

openalex publication_date 2025/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The author proves variants of Buchstab's identity on sieve functions, refining the previous work on new iteration rules of Brady. The main tool used in the proof is a special form of combinatorial identities related to the binomial coefficients. As a by--product, the author obtains better inequalities of F_κ(s) and f_κ(s) for dimensions κ> 1.

Related

• On Some Improvements of the Brun-Titchmarsh Theorem. IV
• Real Analytic Methods in the Formulations of some Combinatorial Inequalities
• The square sieve and the large sieve with square moduli
• A generalization of the q-Saalschutz sum and the Burge transform
• The generalized Borwein conjecture. I. The Burge transform