1. On a paper of S S Pillai
- Author
-
Ravindranathan Thangadurai and M. Ram Murty
- Subjects
Combinatorics ,Discrete mathematics ,Correctness ,Argument ,General Mathematics ,Natural number ,Asymptotic formula ,Term (logic) ,Prime (order theory) ,Square (algebra) ,Mathematics - Abstract
In 1935, Erdos 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.
- Published
- 2012