On a paper of S S Pillai
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- 作者：M RAM MURTY (1) murty@mast.queensu.ca
R THANGADURAI (2) thanga@hri.res.in - 关键词：Additive problems – ; applications of Bombieri– ; Vinogradov theorem
- 刊名：Proceedings Mathematical Sciences
- 出版时间：February 2012
- 出版年：2012
- 期刊代码：157_0973-7685
- 类别：mat
- 卷：122
- 期：1
- 页码：1-13
- 数据来源：sp
摘要
In 1935, Erd枚s proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai’s paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai’s paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai’s theorem using the Bombieri–Vinogradov theorem.