Ramanujan, Robin, Highly Composite Numbers, and the Riemann Hypothesis
Jean-Louis Nicolas, Jonathan Sondow
TL;DR
This paper explores the historical development and mathematical connections between Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis, highlighting their equivalences and historical surprises.
Contribution
It provides a comprehensive historical account and clarifies the equivalences related to the Riemann Hypothesis stemming from Ramanujan and Robin's work on highly composite numbers.
Findings
Identifies historical links between Ramanujan, Robin, and the Riemann Hypothesis.
Highlights new historical insights and surprises in the development of these mathematical concepts.
Clarifies the mathematical background of equivalence conditions for the Riemann Hypothesis.
Abstract
We provide an historical account of equivalent conditions for the Riemann Hypothesis arising from the work of Ramanujan and, later, Guy Robin on generalized highly composite numbers. The first part of the paper is on the mathematical background of our subject. The second part is on its history, which includes several surprises.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · History and Theory of Mathematics