M Ram Murty
Articles written in Proceedings – Mathematical Sciences
Volume 97 Issue 1-3 December 1987 pp 247-250
Let a∈Q and denote by
Volume 104 Issue 1 February 1994 pp 93-98 Obituary note
Zagier constructed a cusp form for each weight
Volume 122 Issue 1 February 2012 pp 1-13
In 1935, Erdös 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.