The function that bears Riemann’s name was studied earlier by Euler. For a real number $s$ greater than 1, the series $$\zeta(s) = 1 + \frac{1}{2^s} + \frac{1}{3^s} + \frac{1}{4^s} + \cdots = \sum_{n=1}^{\infty}\frac{1}{n^s}$$converges. Euler computed several of its values, such as $\zeta(2) = \frac{\pi^2}{6}$, the solution of the Basel problem. Euler’s product Euler’s deepest discovery, of 1737, was that the same function can be written as a product over the prime numbers: