Euler zeta function

Euler studied the sum

for integers s > 1 (clearly

(1) is infinite). Euler discovered a formula relating

(2k) to the Bernoulli numbers yielding results such as

and

What has this got to do with the primes? The answer is in the following product taken over the primes p (also discovered by Euler):

Euler wrote this as

See Also: RiemannZetaFunction

Related pages (outside of this work)