2006年
Approximating the number of integers without large prime factors
MATHEMATICS OF COMPUTATION
- 巻
- 75
- 号
- 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
- ID情報
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- ISSN : 0025-5718
- Web of Science ID : WOS:000236723300027