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arXiv · 2504.07974

A note on variants of Buchstab's identity

Runbo Li
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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 $F_{\kappa}(s)$ and $f_{\kappa}(s)$ for dimensions $\kappa > 1$.

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Runbo Li. 2025-03-26. A note on variants of Buchstab's identity. https://arxiv.org/abs/2504.07974

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