Prime Numbers and Highly Composite Numbers

  • M. Ram Murty
  • V. Kumar Murty


In 1915, Ramanujan wrote a long paper on “highly composite numbers.” This paper gives us a general method to analyse the growth of arithmetic functions. It is curious that this paper finds no discussion in Hardy’s “Twelve lectures.” In hindsight, we learn that the theory has a rich structure as well as interplay with other parts of number theory. Moreover, it is intimately connected with prime number theory and even the Riemann hypothesis.


Prime Number Arithmetic Progression Maximal Order Riemann Hypothesis Prime Number Theorem 
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© Springer India 2013

Authors and Affiliations

  • M. Ram Murty
    • 1
  • V. Kumar Murty
    • 2
  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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