The combinatorics behind number-theoretic sieves
type: Item
instance of: scholarly article
title: The combinatorics behind number-theoretic sieves
zbMATH Open document ID: 0915.11046
author: Timothy Y. Chow
published in: Advances in Mathematics
publication date: 1999-06-23T00:00:00Z
review text: Following \textit{G.-C. Rota}'s extension of the Möbius function to a general lattice, described in [Z. Wahrscheinlichkeitstheorie Verw. Geb. 2, 240-368 (1964; Zbl 0121.02406)], the author extends the notions of upper and lower bound sieve to this context. He supplies an extension of Selberg's upper bound sieve to this more general situation. As he notes, the proof in the number-theoretic case carries over almost word for word. A number of situations are described where one hopes that this idea might be applied. No details of any such application are given; the author indicates that he hopes to do this at a later date. A note added in proof acknowledges the earlier paper on the same theme by \textit{R. J. Wilson} [Colloq. Math. Soc. János Bolyai 4, 1141-1149 (1970; Zbl 0213.33203)].
reviewed by: George Greaves
Mathematics Subject Classification ID: 11N35
Mathematics Subject Classification ID: 05A20
zbMATH DE Number: 1228410
zbMATH Keywords: sieve
zbMATH Keywords: Moebius function
zbMATH Keywords: lattice
zbMATH Keywords: Selberg's upper bound sieve
MaRDI profile type: Publication
OpenAlex ID: W2045027505
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DOI: 10.1006/AIMA.1998.1748
description: scientific article; zbMATH DE number 1228410