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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Friedlander–Iwaniec theorem ： ウィキペディア英語版 Friedlander–Iwaniec theorem In analytic number theory the Friedlander–Iwaniec theorem〔.〕 (or Bombieri–Friedlander–Iwaniec theorem) asserts that there are infinitely many prime numbers of the form $a^2\; +\; b^4$. The first few such primes are :2, 5, 17, 37, 41, 97, 101, 137, 181, 197, 241, 257, 277, 281, 337, 401, 457, 577, 617, 641, 661, 677, 757, 769, 821, 857, 881, 977, … . The difficulty in this statement lies in the very sparse nature of this sequence: the number of integers of the form $a^2+b^4$ less than $X$ is roughly of the order $X^$. The theorem was proved in 1997 by John Friedlander and Henryk Iwaniec.〔.〕 It uses sieve techniques, in a form which extends Enrico Bombieri's asymptotic sieve. Friedlander–Iwaniec theorem is one of the two keys (the other is the 2005 work of Goldston-Pintz-Yıldırım〔(Primes in Tuples I ), D. A. Goldston, J. Pintz, C. Y. Yildirim, 2005. arXiv.org〕) to the "Bounded gaps between primes"〔 〕 of Yitang Zhang. Iwaniec was awarded the 2001 Ostrowski Prize in part for his contributions to this work.〔("Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize" )〕 This result, however, does ''not'' imply that there are an infinite number of primes of form $a^2+1$, or :2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, … . as the latter is still an unsolved problem (one of Landau's problems). == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Friedlander–Iwaniec theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.