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We derive new results about properties of the Witten zeta function associatedwith the group SU(3), and use them to prove an asymptotic formula for thenumber of n-dimensional representations of SU(3) counted up to equivalence. Ouranalysis also relates the Witten zeta function of SU(3) to a summation identityfor Bernoulli numbers discovered in 2008 by Agoh and Dilcher. We give a newproof of that identity and show that it is a special case of a strongeridentity involving the Eisenstein series.

On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function