I'll discuss an asymptotic formula for the number of n-dimensional representations of the group SU(3), analogous to the famous asymptotic formula for the number of integer partitions proved by Hardy and Ramanujan in 1918, which answers the same question for the case of SU(2). The proof requires analyzing the properties of the so-called Witten zeta function associated with SU(3). An interesting corollary is the discovery of a sequence of "trivial zeros" of this zeta function, which have a close connection to a summation identity for the Bernoulli numbers. Mysteriously, a sequence of numbers associated with alternating sign matrices, well-known objects from combinatorics, also appears.