Prime Numbers and Highly Composite Numbers

M. Ram Murty and V. Kumar Murty
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
V. Kumar Murty: University of Toronto, Department of Mathematics

Chapter Chapter 10 in The Mathematical Legacy of Srinivasa Ramanujan, 2013, pp 135-147 from Springer

Abstract: 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.

Keywords: Prime Number; Arithmetic Progression; Maximal Order; Riemann Hypothesis; Prime Number Theorem (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-0770-2_10

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DOI: 10.1007/978-81-322-0770-2_10

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