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 $\sum _{d|n}d$. Then the Riemann Hypothesis is equivalent to the statement that, for $n\ge 1$, $\sigma (n)\le H_n+\ln (H_n)e^{H_n}$ .

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!