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math.HO2012
Ramanujan, Robin, Highly Composite Numbers, and the Riemann Hypothesis
Jean-Louis Nicolas, Jonathan Sondow
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 number…
math.NT2012
Maximal product of primes whose sum is bounded
Marc Deléglise, Jean-Louis Nicolas
If n is a positive integer, let h(n) denote the maximal value of the product of distinct primes whose sum does not exceed n. We give some properties of this function h and describe…
math.NT2012★ 2 cited
Small values of the Euler function and the Riemann hypothesis
Jean-Louis Nicolas
Let $\vfi$ be Euler's function, $\ga$ be Euler's constant and be the product of the first primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\lo…