Some problems of 'partitio numerorum', III On the expression of a number as a sum of primes
Some problems of 'partitio numerorum', III On the expression of a number as a sum of primes
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DOI：
10.1007/bf02403921
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发表时间：
1923-01-01
期刊：
影响因子：
3.7
通讯作者：
Littlewood, JE
中科院分区：
文献类型：
--
作者：
Hardy, GH;Littlewood, JE
~。导言。哥德巴赫在1742年6月7日给欧拉的一封信中断言，每个偶数2m都是o/2个奇素数的和，这一命题通常被描述为戈德巴赫定理。毫无疑问，这个定理是正确的，而且当m很大时，表示的数量是很大的；但所有试图获得证明的尝试都完全没有成功。事实上，从来没有人证明过每个数(或每个大数，也就是说，从某一点开始的任何数)都是素数之和，或者是素数之和；而且这个问题最近被归类为“beim gegenwiirtigen Stande de Wissensehaft unangreifbar”。~在这本回忆录中，我们借助于我们在《Additiver Zahlentheorie》中的新的先验方法来解决这个问题。~我们没有解决它：我们没有E·朗道，《Gel6ste und ungelOste Probleme Ader Theorie der Primahzlverilung der RiemannschenZetafuntion》，L第五届国际数学家大会论文集
~. Introduction. zI It was asserted by GOLDBACH, in a letter to" EuLER dated 7 June, 1742, that every even number 2m is the sum o/two odd primes, ai~ d this propos ition has generally been described as' Goldbach's Theorem'. There is no reasonable doubt that the theorem is correct, and that the number of representations is large when m is large; but all attempts to obtain a proof have been completely unsuccessful. Indeed it has never been shown that every number (or every large number, any number, that is to say, from a certain point onwards) is the sum of xo primes, or of i oooooo; and the problem was quite recently classified as among those'beim gegenwiirtigen Stande der Wissensehaft unangreifbar'.~ In this memoir we attack the problem with the aid of our new transcendental method in'additiver Zahlentheorie'.~ We do not solve it: we do not i E. LANDAU,'Gel6ste und ungelOste Probleme aus der Theorie der Primzahlverteilung und der Riemannschen Zetafunktion', l~'oceedings of the fifth Infernational Congress of Mathematicians,