• Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • Keywords


      Additive problems; applications of Bombieri–Vinogradov theorem.

    • Abstract


      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.

    • Author Affiliations


      M Ram Murty1 R Thangadurai2

      1. Department ofMathematics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
      2. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2022-2023 Indian Academy of Sciences, Bengaluru.