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Prime Numbers and Highly Composite Numbers

In: The Mathematical Legacy of Srinivasa Ramanujan

Author

Listed:
  • M. Ram Murty

    (Queen’s University, Department of Mathematics and Statistics)

  • V. Kumar Murty

    (University of Toronto, Department of Mathematics)

Abstract

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.

Suggested Citation

  • M. Ram Murty & V. Kumar Murty, 2013. "Prime Numbers and Highly Composite Numbers," Springer Books, in: The Mathematical Legacy of Srinivasa Ramanujan, edition 127, chapter 0, pages 135-147, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-0770-2_10
    DOI: 10.1007/978-81-322-0770-2_10
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