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Aperiodvent, Day 23: The Robin-Lagarias Theorem

Today’s entry is a Theorem of the Day:

The Robin-Lagarias Theorem:

Let $H_n$ denote the n-th harmonic number $\sum_{i=1}^n \frac{1}{i}$ , and let $\sigma(n)$ denote the divisor function $\sum_{d \vert n} d$. Then the Riemann Hypothesis is equivalent to the statement that, for $n \geq 1$, $\sigma(n) \leq H_n + \ln(H_n) e^{H_n}$ .

While this isn’t the traditional Christmas kind of Robin, it is equivalent to the Riemann Hypothesis. For more information, see the full listing at Theorem of the Day: the Robin-Lagarias Theorem.

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!



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