論文

査読有り 筆頭著者 責任著者
2006年

Approximating the number of integers without large prime factors

MATHEMATICS OF COMPUTATION
  • K Suzuki

75
254
開始ページ
1015
終了ページ
1024
記述言語
英語
掲載種別
研究論文(学術雑誌)
出版者・発行元
AMER MATHEMATICAL SOC

Psi( x, y) denotes the number of positive integers <= x and free of prime factors > y. Hildebrand and Tenenbaum gave a smooth approximation formula for Psi( x, y) in the range (log x)(1+epsilon) < y <= x, where epsilon is a fixed positive number <= 1/2. In this paper, by modifying their approximation formula, we provide a fast algorithm to approximate.( x, y). The computational complexity of this algorithm is O(root(log x)(log y)). We give numerical results which show that this algorithm provides accurate estimates for Psi(x, y) and is faster than conventional methods such as algorithms exploiting Dickman's function.

リンク情報
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000236723300027&DestApp=WOS_CPL
ID情報
  • ISSN : 0025-5718
  • Web of Science ID : WOS:000236723300027

エクスポート
BibTeX RIS