On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the
Witten zeta function
- Author(s): Romik, Dan;
- et al.
Published Web Locationhttps://arxiv.org/pdf/1503.03776.pdf
We derive new results about properties of the Witten zeta function associated with the group SU(3), and use them to prove an asymptotic formula for the number of n-dimensional representations of SU(3) counted up to equivalence. Our analysis also relates the Witten zeta function of SU(3) to a summation identity for Bernoulli numbers discovered in 2008 by Agoh and Dilcher. We give a new proof of that identity and show that it is a special case of a stronger identity involving the Eisenstein series.