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Prime Numbers and Highly Composite Numbers

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The Mathematical Legacy of Srinivasa Ramanujan

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada

    M. Ram Murty

  2. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

    V. Kumar Murty

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  1. M. Ram Murty
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  2. V. Kumar Murty
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Murty, M.R., Murty, V.K. (2013). Prime Numbers and Highly Composite Numbers. In: The Mathematical Legacy of Srinivasa Ramanujan. Springer, India. https://doi.org/10.1007/978-81-322-0770-2_10

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